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# MCQs on Basic Equations of Compressible Flow

Which among the following is the formula for continuity equation?

a) ρ(x)V(x)A(x) = Constant

b) A(x) = Constant

c) ρ(x)V(x) = constant

d) P(x)V(x) = constant

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a

Explanation: Continuity equation for a steady one-dimensional flow is ρ(x)V(x)A(x) = Constant. Where ρ = Density of the fluid flow. V = the volume of the fluid flow. And, A = Area of the fluid flow through the cross section of pipe.

What is v2/2 in the equation for a control volume in space?

a) Potential energy per unit mass

b) Kinetic energy per unit mass

c) Thermal energy per unit mass

d) Mechanical energy per unit mass

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b

Explanation: According to the first law of thermodynamics, the equation for control volume in space is derived. v2/2 in the equation for a control volume in space is the kinetic energy per unit mass. Therefore, option b is the right choice.

Sum of enthalpy and kinetic energy remains a constant in __________

a) Polytropic flow

b) Isentropic flow

c) Adiabatic flow

d) Mechanical flow

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c

Explanation: The sum of enthalpy and kinetic energy remains a constant in adiabatic flow. It performs a similar role that internal energy performs during a nonflowing system. Thus, the correct option is Adiabatic flow.

Eddy viscosity is a turbulent transfer of _________

a) Fluid

b) Heat

c) Momentum

d) Pressure

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c

Explanation: Eddy viscosity is a turbulent transfer of momentum by eddies. It gives rise to an internal fluid friction. It is in analogous to the action of molecular viscosity in laminar fluid flow. Eddy viscosity takes place on a large scale.

Which among the following is the equation for Bernoulli?

a) Tds = dh – vdp

b) Tds = dh

c) Tds = dh + vdp

d) Tds = dh/vdp

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a

Explanation: For an adiabatic frictionless flow, the Bernoulli’s equation is identical to its energy equation. The Bernoulli’s equation after integrating changes to Tds = dh – vdp. Thus, the correct option is a.

For an isentropic flow ________

a) Enthalpy = 0

b) Entropy = 0

c) Pressure = 0

d) Temperature = 0

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b

Explanation: For an isentropic flow in Tds = dh – vdp, the entropy reduces to zero. That is, the change in entropy value for any isentropic flow (ds)=0. Thus, the correct option is Entropy = 0.

Which among the following is Euler’s equation?

a) VdV/dh = 0

b) VdV – dh = 0

c) VdV + dh = 0

d) dh – V = 0

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c

Explanation: The Euler’s equation is given as VdV+dh=0. Where V = volume of the fluid flow and h = enthalpy of the fluid flow. This is identical to the adiabatic form of the energy equation. Thus, the option is VdV + dh = 0.

Which among the following is the formula for momentum principle?

a) pv = 0

b) p1p2 = 0

c) P1V1 + P2V2 = 0

d) P1A1+P2A2 + F = mV2mV1

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d

Explanation: For a finite control of volume between two sections, section 1 and section 2, the momentum principle is P1A1 + P2A2 + F = mV2mV1. Where F = component of resultant force exerted on the fluid walls.

Define Stagnation temperature.

a) The temperature at zero velocity

b) The temperature at zero pressure

c) The temperature at zero heat transfer

d) The temperature at zero volume

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a

Explanation: The stagnation point is the point at which the properties of the fluid are obtained at a local flow where the velocity of the fluid is zero isentropically. Thus, the correct choice for stagnation temperature is ‘a’.

What is the viscosity of water at 30oC?

a) 80.1

b) 0.801

c) 801

d) 0.081

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b

Explanation: A graph is plotted with temperature in the x-axis and dynamic viscosity in the y-axis. With the increase in pressure the viscosity decreases. It corresponds to an informal concept of thickness.