Fluid Mech Sem 2

Question 1

State Bernoulli’s equation

Answer 1

1/𝟐𝝆𝑽²+𝒑+𝝆𝒈z = constant along a streamline

Question 2

What is a streamline?

Answer 2

A line used to represent particle paths in a steady flow

Question 3

What is fundamental about streamlines in an inviscid flow?

Answer 3

Energy is conserved along them

Question 4

What are the 3 energies included in Benoulli’s equation?

Answer 4

Kinetic energy
Potential energy
Pressure ‘energy’

Question 5

What term in the Bernoulli equation can often be neglected?

Answer 5

The potential energy, 𝝆𝒈z in AIR BUT NOT IN WATER
In air, for the height change to be big enough you’ve probably moved far enough so the density of air has also changed
But in water the pressure changed add up much more quickly so cannot be neglected

Question 6

What is Head, H?

Answer 6

The height to which the water could be pumped if all the pressure and kinetic energy were converted to potential energy

Question 7

Write the Bernoulli equation in terms of head (divide by 𝝆𝒈)

Answer 7

H = 𝑝/𝜌𝑔+𝑉²/2𝑔+𝑧

Question 8

What does Bernoulli’s equation NOT model?

Answer 8

The losses eg due to friction in pipes (so the Head will be lower than suggested)

Question 9

What is stagnation pressure?

Answer 9

The pressure available if you stagnate the flow

Question 10

What is the dynamic pressure?

Answer 10

The pressure available in kinetic energy

Question 11

What is the equation to find stagnation pressure?

Answer 11

p₁+ 1/2 𝜌(𝑉∞)² = p₀
p₁ is static pressure - measured pressure

Question 12

When can you use bernoulli?

Answer 12

Bernoulli’s equation can only be used in situations where you can draw a
streamline, and where there is no loss. This means that Bernoulli’s equation
cannot be applied to unsteady flows, mixing, flows with non-negligible
viscosity etc.

Question 13

Bernoulli cannot be applied to flows where the density ______ This includes flows with velocities over Mach _________

Answer 13

varies
0.25-3

Question 14

What is the equation to find dynamic pressure

Answer 14

1/2 𝜌(𝑉∞)² = p₀ - p₁
Pressure from kinetic energy

Question 15

When can air be considered incompressible -> can use Bernoulli?

Answer 15

Below speed of 85 - 100m/s
(below Mach 0.25 - 0.3)

Question 16

How does a pitot-static stube measure the velocity of a flow?

Answer 16

Via the dynamic pressure, which is the difference between the stagnation and static pressure

Question 17

What causes losses in realistic flows?

Answer 17

Mixing / Expansion, Pipe Friction, Pipe Bends / Inlets / Exits

Question 18

How do you write bernoulli whilst accounting for external work?

Answer 18

1/𝟐𝝆𝑽₁²+𝒑₁+𝝆𝒈z₁ + Eᵢₙ - Eₗₒₛₛ = 1/𝟐𝝆𝑽₂²+𝒑₂+𝝆𝒈z₂

Question 19

How do you calculated the work added by a pump in pascals?

Answer 19

Eₚᵤₘₚ = Δp₀,ₚᵤₘₚ=𝝆𝒈ΔHₚᵤₘₚ

Question 20

How do you calculate the power of a pump?

Answer 20

W dot = ˙Wₚᵤₘₚ= QΔp₀,ₚᵤₘₚ = ṁ𝒈ΔHₚᵤₘₚ

Question 21

If there is a difference in momentum between the flow entering and leaving a control volume, what must have happened?

Answer 21

A force must have been applied

Question 22

Where does the force that changes the momentum in a control volume usually come from?

Answer 22

A change in pressure and/or an external force

Question 23

What equation (name) is used to apply conservation of momentum to a control volume?

Answer 23

Steady Flow Momentum Equation

Question 24

What is the Steady Flow Momentum Equation WRITE ON FORMULA SHEET

Answer 24

Fₙₑₜ = Fₓ + pᵢₙAᵢₙ - pₒᵤₜAₒᵤₜ =ṁₒᵤₜvₒᵤₜ - ṁᵢₙvᵢₙ

Question 25

What is the technique to apply the SFME

Answer 25

1. Draw a control volume, note positive x direction 2. Mark on the pressure on all the control volume boundaries, usually in gauge pressure 3. Mark on the momentum fluxes in and out 4. Write down the SFME 5. Use continuity and/or Bernoulli to find any unknowns 6. Sub in values to find the external force applied to the fluid Fₓ 7. If necessary find the force on the surroundings, Rx = -Fₓ [PUT THIS ON FORMULA BOOK]

Question 26

How do you apply SFME in 2 or 3 directions?

Answer 26

Calculate the components of force, momentum and pressure in each direction

Question 27

How can you make your life easier when solving problems using the SFME?

Answer 27

Choosing a different co-ord system (make sure they are all perpendicular tho)

Question 28

How do you find the momentum flux of a non uniform flow?

Answer 28

M` = ∫ 𝜌u² dA NOT the same as multiplying the mass flow rate by the average velocity

Question 29

What does the momentum correction factor, β, do? WRITE MOMENTUM FLUX EQUATION ON CHEAT SHEET WITH β

Answer 29

Compares the momentum of a non-uniform flow with that of a uniform flow with the same total mass flux.

Question 30

What is it important to consider when given a problem where the flow is not constrained?

Answer 30

Consider flow through all surfaces of the control volume

Question 31

What is present in a flow with curved streamlines?

Answer 31

A pressure variation normal to the streamlines

Question 32

For curved streamlines, which side has high pressure and which side has the low pressure?

Answer 32

High pressure is on the outer (convex) side of the curve and low pressure on the inner (concave) side

Question 33

What is the equation that explain the pressure gradient for streamlines?

Answer 33

dp/dr = ρ(V²/R) = ρω²R

Question 34

What can be said about parallel streamlines?

Answer 34

They have an 'infinite' radius of curvature so there is no pressure gradient, constant across parallel streamlines

Question 35

What can you do if you choose streamlines that have come from the same source?

Answer 35

You can apply Bernoulli

Question 36

What does streamline curvature mean for aerofoils?

Answer 36

They generate lift through the pressure difference, not from the air travelling over both surfaces in the same time

Question 37

What does the Magnus effect describe?

Answer 37

The generation of a lift force by a spinning object. The spinning of the object causes the flow to be faster on one side than the other and thus generates a pressure difference perpendicular to the flow

Question 38

What does the Coanda effect describe?

Answer 38

The tendency of a jet of fluid to follow a curved surface

Question 39

How is flow measured in a pipe?

Answer 39

Using a venturi meter or an orifice plate

Question 40

What are the differences between a venturi meter and an orifice plate?

Answer 40

Orifice plates are much easier and cheaper to construct, but cause a large amount of energy loss due to the rapid expansion. A venturi meter has a very low loss, but its discharge coefficient will only be constant over a small range of flow rates

Question 41

What are the options to measure flow where the flow is not constrained by a pipe such as a wind tunnel or aeroplane?

Answer 41

The most common device is the Pitot-static tube. Alternatively, more expensive and more dangerous laser-based systems can be used to perform non-invasive measurements of the flow

Question 42

What is another option if measuring a flow proves to be difficult?

Answer 42

The flow can be visualised instead using smoke or paint

Question 43

What are 3 important things to remember in Fluid Mech?

Answer 43

- Mass is always conserved - If the momentum of a fluid changes when it passes through a control volume, a force must have been exerted on the fluid - You can only use Bernoulli if you can draw a streamline