Fluid Dynamics

Question 1

Absolute Pressure formula

Answer 1

P = P_o + pgz

z: depth
p: density of fluid

P_o: ambient pressure

Think of swimming pool

Question 2

Gauge Pressure formula

Answer 2

P_gauge = P_absolute - P_atm

P_gauge = P_o + pgz - P_atm

think measuring gauge pressure in tires

Question 3

What is Pascal’s principle?

Answer 3

for incompressible fluids, a pressure change is transmitted through the fluid and to the vessel walls without being diminished

Question 4

Buoyancy force formula

/ Archimedes Principle formula

Answer 4

F_b = m_{displaced lfluid}g

F_b = p_fluid*V_{displaced fluid}*g

Buoyancy force is equal to the weight of the displaced fluid

Question 5

What is cohesion, surface tension, and adhesion?

Answer 5

Cohesion is attractive forces between molecules of a liquid (not different liquids) –> results in surface tension

adhesion is attractive forces molecules have towards molecules of another substance

Question 6

What is viscosity?

Answer 6

resistance of a fluid to flow

low viscosity: less resistance to flow, more like ideal fluids, laminar flow

more viscous liquids lose more energy while flowing

Question 7

What is laminar flow and what law/equation is used to calculate laminar flow rate through a confined space?

Answer 7

smooth, orderly, layers of fluid flowing parallel to each other

Given constant flow rate, for a small decrease in radius, there is a large increase in pressure gradient.

Question 8

What is the formula for critical speed of a fluid in a tube?

Answer 8

N_R: Reynolds number

D: diameter of tube

eta: viscosity of the liquid

Question 9

What is critical speed?

Answer 9

the speed at which unobstructed fluid flow becomes turbulent

at critical speed, laminar flow only occurs at the thin layer of fluid adjacent to the vessel wall, the boundary layer

Question 10

What is the difference ebtween flow rate and linear speed of a fluid? Does changing cross-sectional area affect either?

Answer 10

flow rate is the volume of fluid traveled per unit time. Flow rate is constant for a closed system, and flow rate is not affected by cross-sectional area.

Linear speed is the linear displacement of fluid particles per unit time. Linear speed is affected by cross-sectional area.

Question 11

What is the equation that relates flow rate to linear speed?

Answer 11

Q = v₁A₁ = v₂A₂

This is the continuity equation. liner speed increases with decreasing cross-sectional area, but flow rate stays the same.

Question 12

What is Bernoulli’s equation and what does it mean?

identify the terms for dynamics pressure and static pressure

Answer 12

the sum of dynamic and static pressure of an incompressible fluid is constant when in a closed container without viscous drag

P₁ + 0.5pv₁² + pgh₁ = P₂ +0.5pv₂² + pgh₂

P: absolute pressure (P_o + pgz, where z is depth)

static pressure: P + pgh (h, height of fluid above point)

dynamic: pressure: 0.5pv² (think kinetic energy)

Question 13

What is the Venturi effect?

Answer 13

when cross-sectional area decreases, linear speed increases (continuity equation). Since linear speed increases, dynamic pressure increases and static pressure decreases (Bernoulli’s equation). Due to the decrease in static pressure (ie. decrease in absolute pressure), a column of fluid sticking up from the Venturi tube will be lower.