## GATE ME solved Questions on Flow through pipes (Fluid Mechanics)

**Question #1**

The instantaneous stream-wise velocity of a turbulent flow is given as follows:

$u(x,y,z,t)=\bar{u}(x,y,z,t)+{\mu }'(x,y,z,t)$

The time-average of the fluctuating velocity

{u }'(x,y,z,t) is

(A) ${u}’/2$

(B) $-u/2$

(C) zero

(D) $u/2$

**[GATE 2016 Set 1, 1 mark]**

**Question #2**

Consider a fully developed steady laminar flow of an incompressible fluid with viscosity $\mu$ through a circular pipe of radius R. Given that the velocity at a radial location of R/2 from the centerline of the pipe is U_{1}, the shear stress at the wall is $K\mu U_1/R$, where K is __________

**[GATE 2016 Set 3, 2 marks]**

**Question #3**

Consider fully developed flow in a circular pipe with negligible entrance length effects. Assuming the mass flow rate, density and friction factor to be constant, if the length of the pipe is doubled and the diameter is halved, the head loss due to friction will increase by a factor of

(A) 4 (B) 16 (C) 32 (D) 64

**[GATE 2015 Set 1,1 mark ]**

**Question #4**

The head loss for a laminar incompressible flow through a horizontal circular pipe is h_{1}. Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is h_{2}. The ratio h_{2}/h_{1} is

(A) 1

(B) 4

(C) 8

(D) 16

**[GATE 2015 Set 2, 2 marks]**

**Question #5**

For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe of radius 5 cm, the axial pressure gradient is −10 Pa/m. The magnitude of axial velocity (in m/s) at a radial location of 0.2 cm is _______

**[GATE 2015 Set 2, 2 marks]**

**Question #6**

Water flows through a 10 mm diameter and 250 m long smooth pipe at an average velocity of 0.1 m/s. The density and the viscosity of water are 997 kg/m^{3} and 855×10^{−6} N.s/m^{2}, respectively. Assuming fully-developed flow, the pressure drop (in Pa) in the pipe is _______

**[GATE 2015 Set 2, 2 marks]**

**Question #7**

Water flows through a pipe having an inner radius of 10 mm at the rate of 36 kg/hr at 25°C. The viscosity of water at 25°C is 0.001 kg/m.s. The Reynolds number of the flow is _______

**[GATE 2015 Set 2, 2 marks]**

**Question #8**

Couette flow is characterized by

(A) steady, incompressible, laminar flow through a straight circular pipe

(B) fully developed turbulent flow through a straight circular pipe

(C) steady, incompressible, laminar flow between two fixed parallel plates

(D) steady, incompressible, laminar flow between one fixed plate and the other moving with a constant velocity

**[GATE 2015 Set 3, 1 mark]**

**Question #9**

Three parallel pipes connected at the two ends have flow-rates Q_{1}, Q_{2} and Q_{3} respectively, and the corresponding frictional head losses are h_{L1}, h_{L2} and h_{L3} respectively. The correct expressions for total flow rate (Q) and frictional head loss across the two ends (h_{L}) are

(A)$Q=Q_1+Q_2+Q_3;\ h_L=h_L1+h_L2+h_L3$

(B)$Q=Q_1+Q_2+Q_3;\ h_L=h_L=h_L2=h_L3$

(C)$Q=Q_1=Q_2=Q_3;\ h_L=h_L1+h_L2+h_L3$

(D)$Q=Q_1=Q_2=Q_3;\ h_L=h_L1=h_L2=h_L3$

**[GATE 2015 Set 3, 1 mark]**

**Question #10**

For a fully developed flow of water in a pipe having diameter 10 cm, velocity 0.1 m/s and kinematic viscosity 10^{−5} m^{2}/s, the value of Darcy friction factor is _______

**[GATE 2014 Set 1, 2 marks]**

**Question #11**

A fluid of dynamic viscosity 2 × 10^{−5} kg/m.s and density 1 kg/m^{3} flows with an average velocity of 1 m/s through a long duct of rectangular (25 mm × 15 mm) cross-section. Assuming laminar flow, the pressure drop (in Pa) in the fully developed region per meter length of the duct is _______

**[GATE 2014 Set 2, 2 marks]**

**Question #12**

Consider the turbulent flow of a fluid through a circular pipe of diameter, D. Identify the correct pair of statements.

I. The fluid is well-mixed

II. The fluid is unmixed

III. ReD < 2300

IV. ReD > 2300

(A)I, III

(B) II, IV

(C) II, III

(D) I, IV

**[GATE 14 S3, 1 mark]**

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