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# MCQs on Flow of Viscous Fluid Through Circular Pipes

For a fully-developed pipe flow, how does the pressure vary with the length of the pipe?

a) Linearly

b) Parabolic

c) Exponential

d) Constant

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a

Explanation: In a zero acceleration fully-developed flow in a pipe, the pressure gradually decreases linearly along the length of the pipe. Hence, the pressure variation is said to be linear.

When a problem states “The velocity of the water flow in a pipe is 20 m/s”, which of the following velocities is it talking about?

a) RMS velocity

b) Average velocity

c) Absolute velocity

d) Relative velocity

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b

Explanation: In a pipe-flow, the velocity is always referred to the average velocity. There may be a case where all water particles move in the same direction with 20 m/s, then the average velocity will be equal to absolute velocity. But, this is only a special case. Hence, average velocity will always be true.

Which of the factors primarily decide whether the flow in a circular pipe is laminar or turbulent?

a) The Prandtl Number

b) The Pressure gradient along the length of the pipe

c) The dynamic viscosity coefficient

d) The Reynolds Number

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d

Explanation: High Reynolds number flows (> 4000) are turbulent flows, whereas low Reynolds number flows (< 2100) are laminar flows. The viscosity coefficient is a part of the Reynolds number, but isn’t the only criteria for decision.

How is Reynolds number defined as?

a) Ratio of pressures in the inlet to the outlet of a pipe

b) The product of velocity of the flow and the diameter of the pipe, divided by the kinematic viscosity of fluid

c) The product of density of the fluid, velocity of the flow and the diameter of the pipe, divided by the dynamic viscosity of fluid

d) Ratio of inertia force to viscous force

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d

Explanation: The question demands the definition and not the commonly used formula of Reynolds number. Some of them denote the formula of Reynolds number. The definition of Reynolds number is the ratio of inertia force to viscous force in a pipe flow.

A circular pipe of radius 7 cm is used for water flow transmission. This pipe is moulded into another pipe with a square cross-section keeping the length same. (Ignore the thickness of the pipe). Calculate the hydraulic diameter of the moulded pipe. (Take π = 22/7).

a) 11 cm

b) 7 cm

c) 3.5 cm

d) 22 cm

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a

Explanation: The perimeter of the circular cross section and the square cross section will remain the same. Perimeter = 44 cm. Side of square = 11 cm. Hydraulic diameter DH of the pipe is given by 4A/P, where A = Area of cross section and P = wetted perimeter. In case of a square DH = side. Hence, the hydraulic diameter is 11 cm.

Water flows through a circular tube with a velocity of 2 m/s. The diameter of the pipe is 14 cm. Take kinematic viscosity of water 10-6 m2/s and density of water 1000 kg/m3.

a) 2.8*108

b) 2.8*105

c) 2800

d) 28000

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b

Explanation: Reynolds number is given by VD/ν = (2*0.14)/10-6. Density given is extra information. One shouldn’t be confused by that.

The Reynolds number is found out for a flow in a circular pipe. This circular pipe is moulded into a square pipe, keeping length of the pipe same. Ignore the thickness of the pipe. The Reynolds number changes by __________

a) 57% decrease

b) 57% increase

c) 43% decrease

d) 43% increase

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b

Explanation: The Reynolds number directly depends upon the hydraulic diameter of the pipe. Suppose the diameter of the pipe is D, the hydraulic diameter of square pipe is 1.57D. Hence, 57% increase.

The flow through a circular pipe is laminar. Now, the fluid through the pipe is replaced with a more viscous fluid and passed through the pipe again with the same velocity. What can we say about the nature of this flow?

a) The flow will become turbulent

b) The flow will be a transition flow

c) The flow will remain laminar

d) The Reynolds number of the earlier flow is required to answer this question

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c

Explanation: A flow through a circular pipe is said to be laminar when the Reynolds number is below 2100. A more viscous fluid would have a higher velocity coefficient, thus reducing the Reynolds number further at the same conditions. Hence, the Reynolds number will be well below 2100. Flow will remain laminar.

What can be the maximum diameter of the pipe for the water flow of velocity 1 m/s (ν = 10-6) to be laminar in nature? Assume Lower critical Reynolds number to be 2100.

a) 2.1 mm

b) 21 mm

c) 21 cm

d) 0.21 mm

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a

Explanation: If the Reynolds number of the flow is below its lower critical Reynolds number, the flow is clearly laminar. The maximum diameter can be found for Re = 2100. The diameter comes out to be 2.1 mm.

Which of the following flows have the highest critical Reynolds number (lower)?

a) Flow in a pipe

b) Flow between parallel plates

c) Flow in an open channel

d) Flow around spherical body

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a

Explanation: The approximate lower critical Reynolds number for Flow in a pipe, flow between parallel plates, flow in an open channel and flow around the spherical body are 2000, 1000, 500 and 1 respectively. Hence, the maximum is for internal pipe flow.