Fluids- Compressible Flow

Question 1

At what sort of speeds does compressibility become significant?

Answer 1

Close to sound speed.

Question 2

Rough sound speed in water?

Answer 2

1500m/s. Much faster than fastest submarines or underwater missiles

Question 3

Formula for Mach number?

Answer 3

Ma=u/c
u is characteristic flow velocity
c is speed of sound in the fluid

Question 4

Match different Mach numbers to types of flow

Answer 4

Under 0.3 is incompressible, density variation negligible.
Under 1 is subsonic flow, density effects are significant.
Around 1 is transonic flow, density effects and weak shock waves possible.
Over 1 is supersonic flow, density effects and shock waves possible.
Over 3 is hypersonic flow, strong shock waves possible.

Question 5

Ideal gas law with density

Answer 5

P=ρRT

Question 6

What is the ratio of specific heats (γ or k) for diatomic gases?

Answer 6

1.4 including for air

Question 7

What is true about friction and heat exchange for isentropic processes?

Answer 7

No friction or heat exchange.

Question 8

Express temperature, pressure and density before and after an isentropic process in terms of specific heat ratio

Answer 8

T2/T1=(ρ2/ρ1)^(γ-1)

P2/P1= (ρ2/ρ1)^γ = (T2/T1)^(γ/γ-1)

Question 9

Formula for sound speed

Answer 9

c=rt(γRT)

Often around 340m/s in air

Question 10

What is a stagnation point?

Answer 10

Where a streamline meets an object, around which the flow is passing, and all of the kinetic energy along the streamline is converted into pressure at this point.

Question 11

How are stagnation conditions denoted?

Answer 11

With subscript o (zero)

Question 12

Equation for stagnation temperature over static temperature

Answer 12

To/T=1+((γ-1)/2)Ma^2

Question 13

Relation between stagnation and static pressure and density compared to that for temperature

Answer 13

Stag/stat=same for temp but
Pressure: to power of γ/γ-1
Density: to power of 1/γ-1

Question 14

When are the critical conditions?

Answer 14

Properties when flow is sonic, Ma=1.

Denoted by subscript c or superscript *

Question 15

Ratio of critical to stagnation temperature

Answer 15

T*/To=2/γ+1

Question 16

Ratio of critical to stagnation pressure, density and sound speed in relation to that for temperature

Answer 16

Pressure: to power of γ/γ-1
Density: to power of 1/γ-1
Sound speed: to power of 1/2

Question 17

How to use stagnation to static relation without needing stagnation conditions

Answer 17

Use corresponding formula to find the ratio. Use the ratio for the initial property and the ration for the final property to eliminate stagnation and get relation between initial and final property.

Question 18

What is a nozzle?

Answer 18

A passage having variable section area designed to accelerate or decelerate a flow

Question 19

Where is back pressure?

Answer 19

The pressure outside of and after the nozzle exit

Question 20

How do flow properties in subsonic flow vary as area of nozzle increases?

Answer 20

P increases, T increases, ρ increases, velocity decreases, Ma decreases

Question 21

How do flow properties in supersonic flow vary as area of nozzle increases?

Answer 21

P decreases, temp decreases, density decreases, velocity increases, Ma increases.

Question 22

What is the maximum velocity in a converging nozzle?

Answer 22

Sonic velocity where Ma=1. This occurs at the exit plane (throat) of the nozzle.

Question 23

Describe converging-diverging nozzle and how it works

Answer 23

Attach a diverging flow section to the subsonic nozzle at the throat. If the flow at the throat is sonic, the diverging section can accelerate the flow so it is supersonic and result in Ma>1

Question 24

What can be said about the conditions of a fluid starting in a large tank or reservoir?

Answer 24

They are the stagnation conditions

Question 25

How to get ratio between critical and static conditions?

Answer 25

Product of critical over stagnation and stagnation over static.

Question 26

How to get formula for local nozzle area in relation to throat area

Answer 26

A/A*= product of critical over static ratios for density and velocity.
In compressible flow notes page14

Question 27

Formula for local flow velocity in isentropic flow

Answer 27

u=rt(2Cp(To-T))