1. What is the basic difference between compressible and incompressible fluid flow? Compressible 1. Fluid velocities are appreciable compared with the velocity of sound 2. Density is not constant 3. Compressibility factor is greater than one. 2. Write the steady flow energy equation for an adiabatic flow of air. In an adiabatic flow q = 0. Therefore energy equation becomes. 2 c12 c2 h1 + + gZ1 = h2 + + gZ 2 + Ws 2 2
Incompressible 1. Fluid velocities are small
compared with the velocity of sound 2. Density is constant 3. Compressibility factor is one.
Adiabatic energy equation is h0 = h + ½ c2
3. Define the mach number in terms of bulk modulus of elasticity.
Mach number is a non-dimensional number and is used for the analysis of compressible fluid flows. M= int ertiaforce elasticforce
where K = Bulk modulus of elasticity K = ρ a2
ρAc 2 c = ρAa 2 a
4. Explain the meaning of stagnation state with example.
The state of a fluid attained by isentropically decelerating it to zero velocity at zero elevation is referred as stagnation state. (e.g.) Fluid in a reservoir (or) in a settling chamber.
5. Distinguish between static and stagnation pressures.
In stagnation pressure state, the velocity of the flowing fluid is zero whereas in the static pressure state, the fluid velocity is not equal to zero.
6. Differentiate between the static and stagnation temperatures.
The actual temperature of the fluid in a particular state is known as “static
temperature” whereas the temperature of the fluid when the fluid velocity is zero at zero elevation is known as “stagnation temperature”. T0 T T0 =T+
c2 where 2C p
= static temperature = stagnation temperature = velocity temperature
c2 2C p
7. What is the use of mach number?
Mach number is defined as the ratio between the local fluid velocity to the velocity of sound. i.e. Mach number M=
Localfluidvelocity c = Velocityofsound a
It is used for the analysis of compressible fluid flow problems. Critical mach number is a dimensionless number at which the fluid velocity is equal to its sound velocity. Therefore,
M critical =
c* =1 a*
[ ∴c* = a* ]
Crocco number is a non – dimensional fluid velocity which is defined as the ratio of fluid velocity to its maximum fluid velocity. i.e. C r =
c c max
8. Write down the relationship between stagnation and static temperature interms of the flow, mach number for the case of isentropic flow. T0 γ − 1 2 where, = 1+ M T 2
T0 T M
= stagnation temperature = Static temperature = Mach number.
9. Give the expression of
The expression of
P for an isentropic flow through a duct. P0
T0 γ − 1 2 , but we know that, = 1+ M T 2
T0 P0 = T P
γ −1 γ
P T γ −1 (or ) 0 = 0 P T
P (γ − 1) 2 γ −1 Therefore 0 = 1 + M (or ) P 2
P0 1 γ = P (γ − 1) 2 γ − 1 1 + 2 M
10. Name the four reference velocities that are used in expressing the fluid velocities in non-dimensional form? i. ii. iii. iv. Local velocity of sound a =
2 γ −1
Stagnation velocity of sound a0 =
Maximum velocity of sound C max = a0
Critical velocity of sound / fluid a* = c* =
11. What are the different regions of compressible flow.
The adiabatic energy equation for a perfect gas is derived in terms of fluid velocity © and sound velocity (a). This is then plotted graphically on the c- a co-ordinates, a steady flow ellipse is obtained. The various regions of flow are: (i) (ii) (iii) (iv) (v) Incompressible region (M ≈ 0) Subsonic region Transonic region Supersonic region Hypersonic region (M < 1) (0.8 – 1.2) (M > 1 and M < 5) (M ≥ 5)
12. Define M* and give the relation between M and M*.
It is a non-dimensional mach number and is defined by the ratio between the local fluid velocity to its critical velocity of sound /...