This set of Fluid Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Introduction to Fluid Dynamics”.

1. Which of the following is NOT a type of force considered in the Navier-Stokes equation?

a) Gravity force

b) Pressure force

c) Surface tension force

d) Viscous force

View Answer

Explanation: Gravity, Pressure force and viscous forces together constitute the derivation of the Navier-Stokes equation. Though surface tension force act on a fluid in motion, it is considered to be negligible for the Navier-Stokes equation.

2. Which of the following equations is a result of momentum conservation for inviscid steady flows?

a) Bernoulli’s equation

b) Navier-Stokes equation

c) First law of thermodynamics

d) Euler’s equation

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Explanation: Bernoulli’s equation is an energy conservation equation which is obtained by integration of the Euler equation. Navier-Stokes equation is a force balance equation. The first law of thermodynamics is an energy conservation equation, too. Euler’s equation is a momentum equation. This equation is valid for inviscid steady flows.

3. The Bernoulli’s equation in fluid dynamics is valid for _________

a) Compressible flows

b) Transient flows

c) Continuous flows

d) Viscous flows

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Explanation: To answer this equation, we need to know the assumptions used in Bernoulli’s equation. The Bernoulli’s theorem is only valid for ideal, steady, incompressible, continuous, inviscid and irrotational flows. So, out of the options, only continuous flows fit in the assumptions.

4. A water flows through a pipe at a velocity 2 m/s. The pressure gauge reading is 2 bar. The datum head is given to be 2 m. Find the piezometric head. (Assume all Bernoulli’s assumptions, Density of water = 1000 kg/m^{3}, g = 9.8 m/s^{2}).

a) 22.4 m

b) 22.6 m

c) 20.4 m

d) 20.6 m

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Explanation: Piezometric head is the addition of pressure head and the datum head. The pressure head is given by P/ρg = 20.4 m. The datum head is 2 m, which makes it a total of 22.4 m. The velocity given is extra information.

5. A student wishes to find the velocity of air flowing through a pipe. He has a pressure gauge which displays only the dynamic pressure. The pressure gauge reads 0.018 mm Hg. Assume density of air to be 1.225 kg/m^{3}, find the velocity V of air (ρHg = 13600 kg/m^{3}).

a) 4 m/s

b) 2 m/s

c) 20 m/s

d) 40 m/s

View Answer

Explanation: (0.018 mm Hg * 13.6 * 9.8) = 2.4 bar. Dynamic pressure is given by ρV

^{2}/2. Equating 2.4 bar with dynamic pressure gives V = 2 m/s.

6. If compressibility force and surface tension force are neglected from the Newton’s second law of motion, which of the following equations result?

a) Navier-Stokes equation

b) Euler’s equation

c) Bernoulli’s equation

d) Reynolds equation

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Explanation: The Newton’s second law of motion comprises of 6 forces, namely, gravity, viscosity, pressure, turbulence, surface tension and compressibility forces. Reynolds equation comprises of 4 forces. Surface tension force and compressibility forces are neglected for finding Reynolds equation.

7. What does a pitot tube measure? Upon which principle does a pitot tube work?

a) Pressure, Bernoulli’s principle

b) Velocity, Bernoulli’s principle

c) Pressure, Euler’s equation

d) Velocity, Euler’s equation

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Explanation: Even though a pitot tube may be primarily used to find velocity of a fluid, the Pitot tube measures pressure and not velocity. The Pitot tube works upon the Bernoulli’s principle as it gives us pressure heads.

8. The below figure shows a pipe with a circular cross section of diameter 5 cm on the left end and a square cross section with diagonal 5 cm on the right end. Water enters the left end with a velocity 20 m/s and leaves the right end with a velocity V_{2}. Find V_{2} (neglect losses in the pipe).

a) V_{2} cannot be found as the length of the pipe is not given

b) V_{2} cannot be found as the intermediate cross sections are not given.

c) 31.41 m/s

d) 20 m/s

View Answer

Explanation: Apply continuity equation A

_{1}V

_{1}= A

_{2}V

_{2}. We find that the velocity comes out to be 31.41 m/s. The question can be answered without calculations if the concept is known. V

_{2}neither depends upon the length of the pipe nor on the intermediate cross sections if losses are neglected.

9. In the equation, the unit of E CANNOT be written as ______

a) m^{2}/s^{2}

b) J/kg

c) Pa/m^{3}

d) kg.m/s^{2}

View Answer

Explanation: From the last term, we can deduce that m

^{2}/s

^{2}can be the unit of E. From the first term, we get Pa/m

^{3}and J/kg is equivalent. Kg.m/s

^{2}is not of the same dimension. Hence, that is the correct choice.

10. The best place to place a pitot tube on an aircraft for velocity measurement is just behind the jet engine.

a) True

b) False

View Answer

Explanation: Pitot tube is used for velocity measurement or airspeed measurement of an aircraft. Placing a pitot tube behind the jet engine will give us the speed of the gas rejected by the jet engine instead of the airspeed, hence, giving us erroneous readings. The best placement would be at a point where the speed of air is closest to the airspeed as seen by the aircraft.

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