Fluid Statics & Dynamics

Question 1

Define Fluid

Answer 1

A fluid is any substance that flows freely because its particles are not rigidly attached to one another. Fluids have no repeating crystalline structure.

Question 2

State and explain Pascal’s Principle.

Answer 2

Pascal’s principle states that pressure applied to a confined fluid is transmitted undiminished throughout the confining vessel or system. Fluid force acts equally, at right angles, to every portion of its container surface.

Question 3

Define buoyancy

Answer 3

Buoyancy is defined as the tendency of a body to float or rise when submerged in a fluid. Archimedes’ principle states: “A body wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.” If the density of the body is greater than the fluid it displaces, it sinks. If its density is less, it floats.

Question 4

State and explain Archimedes’ Principle

Answer 4

Archimedes’ principle states: “A body wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.”

Question 5

Define and explain mass flow rate.

Answer 5

The mass flow rate equals the product of the density of the fluid, the cross-sectional area of flow, and average velocity of the fluid. If specific volume is used, mass flow rate is equal to the product of cross-sectional area and average velocity divided by the specific volume of the fluid.

Question 6

Define and explain Volumetric Flow Rate

Answer 6

The volumetric flow rate of a fluid is defined as the volume of the fluid that passes a
reference point per unit time. The volumetric flow rate equals the product of the average velocity of the fluid and the cross-sectional area of flow.

Question 7

How are Volumetric and Mass Flow Rates related?

Answer 7

The mass flow rate and the volumetric flow rate are related by the density or, specific volume, of the fluid.

Question 8

What is viscosity? How does temperature impact viscosity?

Answer 8

• Physically, the viscosity of a fluid is a measure of its resistance to flow when subjected to a shear stress.
• For liquids, viscosity decreases with increasing temperature.
• For gases, viscosity increases with increasing temperature.

Question 9

Describe the two types of fluid flow and their velocity profiles.

Answer 9

The first type is known as laminar, streamline, or viscous flow. The significance of these terms is:

• The fluid particles move in parallel layers where the layers of fluid move
  smoothly over adjacent layers without mixing between them.
• The particles move in definite and observable paths or streamlines.
• The flow is characteristic of viscous fluid or is one in which viscosity plays a significant part.

The second type of flow is known as turbulent flow. It is characterized by irregular motion of the fluid molecules. This velocity profile is flattened at the centerline. For
well-developed turbulent flow, the average velocity is only slightly less than the
centerline velocity.

Question 10

Explain the continuity of fluid flow.

Answer 10

Continuity of fluid flow, or steady flow, occurs when the same mass flow exists everywhere in a pipe, meaning that the same quantity of fluid flows past any two reference points along the pipe in any given time. The continuity fluid flow
equation, when applied to fluid flow, is merely a statement of the continuity of fluid flow.

Question 11

What is the Continuity Equation?

Answer 11

Question 12

State the conditions where Bernoulli’s equation may be applied.

Answer 12

Bernoulli’s equation applies only when the flow of the fluid is treated as ideal, with no fluid friction.

Bernoulli’s equation results from the application of the general energy equation to a steady flow system in which:

1. No heat is transferred to or from the fluid
2. No work is done by or on the fluid
3. No change occurs in the internal energy of the fluid.

Question 13

Write and Explain Bernoulli’s equation in terms of the general energy equation.

Answer 13

PE₁ + KE₁ + P₁V₁ = PE₂ + KE₂ + P₂V₂

Where

PE = potential energy (ft lb_f)

KE = kinetic energy (ft lb_f)

P = pressure (lbf /ft²)

V = volume (ft³)

Question 14

State and explain the Bernoulli Equation with higher detail energy terms.

Answer 14

Question 15

What is the NRC version of the Bernoullie equation?

Answer 15

Question 16

What is elevation head?

Answer 16

Elevation head (z) represents the potential
energy the fluid possesses due to its elevation
above a reference level. It is expressed by
the vertical distance, in feet, between the
reference level and the level of the fluid.

Question 17

What is velocity head?

Answer 17

Velocity head - (V_av)²/ 2g - represents the kinetic energy the fluid possesses due to its velocity. It is the height, in feet, to which the flowing fluid would rise in a column if all of its kinetic energy were converted to potential energy.

Question 18

What is pressure head?

Answer 18

Pressure head (Pυ) represents the PV energy the fluid possesses due to its pressure. It is expressed by the height, in feet, of a column of the fluid whose weight is equivalent to the pressure of the fluid. This pressure is the static pressure, which is the sum of gravity, applied forces, and atmospheric pressure.

Question 19

Explain and distinguish between static pressure, dynamic pressure and total pressure.

Answer 19

Static pressure in a fluid is caused by the motion of molecules. The pressure felt due to flow is called dynamic pressure. These two pressures combine to make up total pressure.

Question 20

Explain and define head loss

Answer 20

It is the conversion of fluid pressure and velocity to heat
energy through friction.

H_f = W_f / m = u₂ - u₁

• H_f = head loss (friction head) due to fluid friction (ft)
• W_f = work done against fluid friction (ft lb_f)
• m = mass (lb_m)
• u₂ = specific internal energy exiting system (Btu/lb_m)
• u₁ = specific internal energy entering system (Btu/lb_m)

Question 21

Explain the effects on head loss from viscosity

Answer 21

(H_f) represents the energy used in overcoming fluid friction. Although this represents a loss of energy from the standpoint of fluid flow, it does not normally represent a loss of total energy from the fluid.

Although the total head of the working fluid decreases because of fluid friction, the internal energy of the fluid, as reflected by its temperature, increases. In an insulated pipe in which there is no heat loss to the surroundings, the head loss equals the internal energy gain.

Question 22

Discuss operational consideration of viscosity as related to head loss

Answer 22

Experimental studies of the flow of liquids in pipes showed that the head loss due to fluid friction varies:

1. Directly with the length of the pipe, since a longer pipe has more surface area
2. Inversely with the diameter of the pipe, since a pipe with a larger diameter has less surface area per unit of cross-sectional area than a pipe with a smaller diameter.
3. Directly with the velocity head of the fluid

Question 23

What is the formula for head loss (H_f) due to friction?

Answer 23

Question 24

Explain and define pump head

Answer 24

Pump head (H<sub>p</sub>) is the head added by the pump to each pound of fluid to maintain
or increase its pressure or velocity.

H_p = W_p / m = h₂ - h₁

H<sub>p</sub> = head added by the pump (ft)
W<sub>p</sub> = work done on the fluid by the pump (ft lbf)
h<sub>2</sub> = specific enthalpy exiting the pump (Btu/lbm)
h<sub>1</sub> = specific enthalpy entering the pump (Btu/lbm)

Specific enthalpy of a working fluid, h, is a property of the fluid which is defined as: h=u+P v where, u= Specific internal energy P= Pressure v= Specific volume

Question 25

What is Bernoulli’s equation with terms for the work done against fluid friction and work of the pump?

Answer 25

Question 26

What is the Reynolds Number

Answer 26

The experimental investigations of Osborne Reynolds in 1883 indicated that for an
noncompressible fluid completely filling a pipe, the mode of flow is determined by:

• Average velocity of the fluid (V_av)
• Diameter of the pipe (d)
• Kinematic viscosity (ν).

Unit analysis, confirmed by experiment, showed that these variables could be grouped to form a unit-less constant called the Reynolds number (N_Re) which can be used to determine the mode of flow.

Question 27

What is the formula for Reynolds Number?

Answer 27

Question 28

For Reynolds numbers less than 2000, what flow is present?

Answer 28

Laminar Flow

Question 29

For Reynolds numbers greater than 3500, what flow is present?

Answer 29

Turbulent Flow

Question 30

For Reynolds numbers between 2,000 and 3,500, what flow is present?

Answer 30

Transitional flow.

Question 31

Describe the relationship between Reynolds number and friction factor.

Answer 31

The value of the friction factor depends on the Reynolds number and the roughness of the pipe.

With laminar flow, the friction factor does not depend on the relative roughness. It is a function of the Reynolds number only.

For Reynolds numbers greater than about 3,500, where turbulent flow prevails, the friction factor is a function of both the Reynolds number and the relative roughness

Question 32

Explain the effects on head loss from friction factor and relative roughness.

Answer 32

The presence of valves and fittings in a line increases the head losses due to fluid friction.

The primary effect of fluid friction and the associated head loss it causes is a pressure drop.

The total head loss is the total energy lost by each lbm of the fluid as it flows through the system. Thus, the fluid exits the system with less flow energy per pound mass than when it entered.

Question 33

Describe fluid flow measurement devices.

Answer 33

The most commonly used types are based on the indirect determination of
flow rate using differential pressure measurements. There are several devices commonly used to convert a measured differential pressure into a flow rate. Most of these devices can be classified as one of three basic designs:

1. pitot tube
2. venturi meter
3. orifice meter

Question 34

What is a Pitot Tube?

Answer 34

A pitot tube compares the pressure at points 1 and 2. The pressure of point 1 is the total pressure. Recall that total pressure is equal to dynamic pressure plus static pressure. The pressure at point 2 is due to static pressure at the sensing point. The static pressures at points 1 and 2 balance out, resulting in the difference in
pressure being equal to the dynamic pressure. Assuming all kinetic energy at point 1 is converted to dynamic pressure allows the use of Bernoulli’s equation to determine velocity. It must also be assumed there is no height difference at the point where pressures are sampled.

Question 35

Calculate Velocity from D/P

Answer 35

Question 36

What is a venturi tube for flow measurement?

Answer 36

A venturi meter is another device used to measure flow. It consists of specially constructed converging and diverging pipe sections,

Question 37

What is the formula for calculating flow through a Venturi?

Answer 37

Question 38

What is an Orifice Meter?

Answer 38

Question 39

Explain why flow measurements must be corrected for density changes.

Answer 39

Not only does density vary inversely with temperature, but the magnitude of the change in density increases as temperature increases. Where the temperature of
the measured fluid changes, flow measurement circuitry uses the mass flow rate continuity equation which allows for density compensation.

Question 40

What is the two-phase flow friction multiplier?

Answer 40

Two-phase flow friction is greater than singlephase flow friction for the same pipe dimensions and mass flow rate. The difference appears to be a function of the type of flow and results from increased flow speeds.

R = H_{f two-phase} / H_{f sat liquid}

Where:
R = two-phase flow friction multiplier (no units)
H_f two-phase = two-phase flow head loss due to friction (ft)
H_f sat liquid = single-phase saturated liquid flow head loss due to friction (ft)

Question 41

What is Slip Ratio?

Answer 41

The average velocities of the two phases are not the same. The average velocity of the liquid phase (V_{av f}) is less than the average velocity of the vapor phase

The slip ratio (SR) of a two-phase flow is a measure of the relative velocities of the liquid and vapor portions.

SR = V_{av g} / V_{av f}
Where:
SR = slip ratio (no units)
V_{av g} = average velocity of the vapor phase (ft/sec)
V_{av f} = average velocity of the liquid phase (ft/sec)

(V_{av g})

Question 42

Explain the purpose of pumps

Answer 42

A pump supplies discharge head to make up for head losses and provide a flow rate.

Question 43

Explain the principles of operation of a centrifugal pump.

Answer 43

It imparts energy to the fluid in its rotor from centrifugal action. Specifically, Fluid enters the impeller in the central portion, called the eye, flows radially outward, and is discharged around the entire circumference into a casing. While flowing through the rotating impeller, the fluid receives kinetic energy from the vanes. This increases both fluid pressure and velocity. Kinetic energy is a large component of
the total energy of the fluid leaving the impeller. It is necessary to reduce fluid velocity and transform a large part of this velocity head into pressure head. This is usually done in the volute casing surrounding the impeller. The area of the volute increases in the direction of flow. Therefore, to maintain a constant flow rate (i.e.
satisfy the continuity equation), the velocity must decrease. Then, from Bernoulli’s equation, as the velocity head decreases, the pressure head increases, and the total head remains constant. Kinetic energy at the exit of the impeller is
converted to flow energy in the volute casing asvelocity decreases and pressure increases.

Question 44

Discuss how the volute acts to decrease flow velocity and increase outlet pressure.

Answer 44

Question 45

Describe how flow rates are controlled for systems containing centrifugal pumps.

Answer 45

The capacity, or flow rate, of a single speed centrifugal pump is
controlled by varying the position of a valve on the discharge side of the pump. A variable speed pump varies the output capacity by changing speeds. Throttling a discharge valve can also be used to change the capacity of a variable speed
centrifugal pump.

Question 46

Define and explain cavitation.

Answer 46

Cavitation is the formation of vapor bubbles in low pressure fluid flow areas and their subsequent collapse as regions of higher pressure are entered.

Question 47

Define and explain Net Positive Suction Head (NPSH) required and available.

Answer 47

The difference between the pump inlet, or suction, pressure and the saturation pressure of the liquid being pumped is called available net positive suction head (NPSH). The required NPSH is the amount of NPSH which must be provided to prevent cavitation, and is determined by the pump manufacturer. If available NPSH is
not greater than required NPSH, the pump will cavitate.

Question 48

Calculate available net positive suction head.

Answer 48

Question 49

What is Recirculation Ratio?

Answer 49

In a steam generator the mixing of the incoming feedwater with the moisture removed by the moisture separators minimizes the temperature difference between the feedwater inlet nozzle and the steam generator shell, which minimizes thermal stress on the nozzles and steam generator shell. It is an additional pre-heating of feedwater before it reaches the tube bundle region.

The ratio of recirculated moisture to the amount of feedwater supplied (and steam produced) is called the recirculation ratio. Under normal conditions, the recirculation ratio is about three-to-one at full power.

Question 50

What is gas binding?

Answer 50

Gas binding is a term used when a pump is filled
with a gas, normally air, instead of the liquid
being pumped. Gas binding is defined as
“excessive air or gas buildup inside a pump
casing”. Under these conditions, the pump
cannot pump the desired liquid. Venting and
filling the pump casing usually eliminate the
problem with gas binding.

Question 51

What is Axial Thrust?

Answer 51

Axial thrust results from unbalanced forces acting along the axis of a pump impeller. These unbalanced forces are caused by the difference between the suction pressure, experienced on one side of the impeller, and the discharge pressure
on the other side. Additionally, differences in the surface area exposed to these pressures contributes to axial thrust. These forces are compensated for by using axial thrust bearings or pressure equalizing holes between regions of uneven hydraulic pressure.

Question 52

What is pump runout?

Answer 52

Pump runout is the term used to describe a
centrifugal pump when it is pumping at its
maximum capacity. This normally occurs when
system pressure drops to its minimum.

Question 53

What is shutoff head?

Answer 53

Shutoff head is the term used when a centrifugal
pump is pumping its fluid with a shut discharge
valve, or against a system pressure equal to or
higher than the pump discharge pressure.

Question 54

Explain how operating a centrifugal pump at shutoff head may cause overheating and describe the methods used to avoid overheating.

Answer 54

The pump adds energy to the liquid in the pump casing, causing the liquid (and pump) temperature to rise. If adequate cooling is not provided, liquid temperature eventually reaches the saturation temperature for the pump suction pressure, causing cavitation and possible damage to the pump. The increased temperature of the pump could also lead to bearing damage or inadequate clearances between moving parts, thus damaging the pump. Most pumps are protected against running at shutoff head by a piping system made of a small diameter pipe and/or an orifice. This minimum flow line taps off between the pump and its discharge valve, and normally returns flow back to the suction source.

Question 55

Describe how flow rates are controlled in systems

containing positive displacement pumps.

Answer 55

Varying the speed of the stroke or varying the length of the stroke.

Question 56

Discuss the relationship between pump speed, head, flow and power without using formulas or calculations.

Answer 56

A plot of discharge head versus capacity, for a given pump speed, is often called the pump characteristic curve.

If the pump speeds up, the entire characteristic curve moves outward, away from the origin. The pump capacity increases by the same factor by which the speed increases, and the pump discharge head increases as the square of the factor by which the speed increases. If the pump operates at constant efficiency, the power required to operate the pump at a new speed increases as the cube of the
factor by which the speed increases.

Question 57

Explain the reason for the shape of a centrifugal pump characteristic curve.

Answer 57

the capacity of a centrifugal pump decreases as
the pressure at the pump discharge increases. At
a particular pressure, called the shutoff head, the
pump moves no fluid at all. If the pump
discharges directly to the atmosphere, the pump
capacity is maximum, called pump runout.

Question 58

Describe how a centrifugal pump chracteristic curve will change with pump speed.

Answer 58

If the pump speeds up, the entire characteristic
curve moves outward, away from the origin.

Question 59

Discuss the characteristic curve for a typical positive displacement pump, and explain the reason for its shape.

Answer 59

A positive displacement pump provides a constant volumetric flow rate as friction losses increase for the same pump speed. The pump head supplied can take any value at constant flow rate.

When friction losses are high, a backpressure builds up in the system, and some high pressure fluid leaks within the pump. Thus, the actual characteristic curve bends to the left at the top, indicating that net flow rate begins to decrease
slightly at some point.

Question 60

Using centrifugal pump characteristic curve and a system chracteristic curve, illustrate how the system operating point changes
due to system throttle valve operation.

Answer 60

The system characteristic curve can be drawn on the same graph as the pump characteristic curve. The point where the curves intersect is the point where pump head equals friction loss. This is where the pump operates, and is thus known as
the operating point.

Partially closing a valve in the flow line increases friction losses and moves the system characteristic curve to the left. A centrifugal pump responds by seeking the operating point. Therefore, the pump head increases and the flow rate decreases. Reopening the valve decreases head loss, and moves the system characteristic
curve back to the right.

Question 61

Explain the results of putting centrifugal pumps in series or parallel combinations.

Answer 61

The characteristic curve for two identical pumps operating in series is
formed by adding the individual pump heads for a given pump capacity.

The characteristic curve for two pumps operating in parallel is found by adding the
individual pump capacities for the given total heads.

Question 62

Evaluate the head added by a pump to determine
pump efficiency and real and ideal work of the pump.

Answer 62

Thus, the head added by a pump (Hp) is a
measure of the pressure rise across the pump.
Pump head is also a measure of the work done
on the fluid by the pump.

See equations…. pgs 43/44

Question 63

Explain the operational implication of water (fluid) hammer.

Answer 63

The best prevention of water hammer is the
THINKING OPERATOR. Operators should
consider the possibility of water hammer
occurring before performing any actions which
could cause a water hammer, especially in offnormal
operating conditions, and take steps to
prevent it.

Question 64

Define and explain a Pressure Spike and pipe whip.

Answer 64

Water hammer may be observed as a system “pressure spike” – a sudden increase in pressure due to energy in the system encountering obstructions.

The uncontrolled movement of pipes/pumps is called “pipe whip”.

Question 65

Explain the importace of proper system venting for pump operation.

Answer 65

Centrifugal pumps are provided with high point
casing vents. The vents allow the pump to be
primed, and to remove the noncondensable gases
that could be trapped in the casing. When a
system is initially filled, the casing vents should
be open before starting the pump, and left open
until a solid stream of liquid comes out.

Question 66

Describe the problems that will occur in Emergency Core Cooling Systems if the pumps are operated at lower than design flow for extended periods of time.

Answer 66

A centrifugal pump should not be operated for extended periods of time at shutoff head. This is especially true for the Emergency Core Cooling System (ECCS) pumps. These pumps could be damaged if run for an extended period of time
with lower than design flow.

The pump adds energy to the liquid in the pump casing, causing the liquid (and pump) temperature to rise. If adequate cooling is not provided, liquid temperature eventually reaches the saturation temperature for the pump suction pressure, causing cavitation and possible damage to the pump. The increased temperature of the pump could also lead to bearing damage or inadequate clearances between moving parts, thus damaging the pump.