GATE-CH-1996-3-3-fm-2mark

Match the following:

• I. 1/7th power law

Answer 1C. inviscid flowA. irrotational flowB. turbulent flowD. laminar flow in pipes

• II. Hagen-Poiseuille equation

Answer 2C. inviscid flowA. irrotational flowB. turbulent flowD. laminar flow in pipes

GATE-CH-1998-2-10-fm-2mark

The dependence of the volumetric flow rate (\(Q\)) on the pressure drop is given by \(\Delta P \propto Q^n\), for different flow regimes. Match the exponent \(n\) to each of the flow regimes given below:

• I. Laminar flow

  
  

Answer 1C. n = 1.0A. n < 0.5D. n > 1.0B. n = 0.5

• II. Turbulent flow

  
  

Answer 2C. n = 1.0A. n < 0.5D. n > 1.0B. n = 0.5

0300-1-fm-1mark

The velocity profile for a Bingham plastic fluid flowing (under laminar conditions) in a pipe is

• parabolic

• flat

• flat near the wall and parabolic in the middle

• parabolic near the wall and flat in the middle

GATE-CH-1988-2-i-fm-1mark

For an ideal fluid flow the Reynolds number is

• infinity

• zero

• one

• 2100

GATE-CH-1988-2-vi-fm-1mark

Consider a duct of square cross section of side ‘\(b\)’. The hydraulic radius is given by

• \(b/8\)

• \(b/4\)

• \(b/2\)

• \(b\)

GATE-CH-1988-2-vii-fm-1mark

A fluid \(A\) of specific gravity 1.0 and viscosity 0.001 N.s/m\(^2\) flows through a horizontal pipe of circular cross section. The fluid \(B\) of specific gravity 2 and viscosity 0.002 N.s/m\(^2\) flows through an identical pipe, with the same average velocity as fluid \(A\). For fluid \(B\), pressure drop per unit length of pipe is

• half that of \(A\)

• same as that of \(A\)

• thrice that of \(A\)

• none of the above

GATE-CH-1989-2-i-a-fm-2mark

For the turbulent flow through a smooth pipe, the following correlation for the friction factor is valid:\(f = c \text {Re}^{-0.2}\) ; where \(c\) is a constant. Suppose that the velocity is increased by 100% the pressure drop:

• increases by less than 100%

• decreases by less than 100%

• increases by more than 100%

• decreases by more than 100%

GATE-CH-1994-1-k-fm-1mark

A Newtonian liquid (\(\rho \) = density, \(\mu \) = viscosity) is flowing with velocity \(v\) in a tube of diameter \(D\). Let \(\Delta P\) be the pressure drop across the length \(L\). For a laminar flow, \(\Delta P\) is proportional to

• \(L\rho v^2/D\)

• \(D\rho v^2/L\)

• \(L\mu v/D^2\)

• \(\mu v/L\)

GATE-CH-1997-1-7-fm-1mark

For the laminar flow of a fluid in a circular pipe of radius \(R\), for a given pressure drop, the Hagen-Poiseuille equation predicts that volumetric flowrate to be proportional to

• \(R\)

• \(R^2\)

• \(R^4\)

• \(R^{0.5}\)

GATE-CH-1997-1-9-fm-1mark

The hydraulic diameter of an annuls of inner and outer radii \(R_i\) and \(R_o\) respectively is

• \(4(R_o-R_i)\)

• \(\sqrt {R_o\cdot R_i}\)

• \(2(R_o-R_i)\)

• \(R_o+R_i\)

GATE-CH-2000-1-11-fm-1mark

For laminar flow of a shear-thinning liquid in a pipe, if the volumetric flow rate is doubled, the pressure gradient will increase by a factor of

• 2

• \(< 2\)

• \(> 2\)

• 1/2

GATE-CH-2000-1-9-fm-1mark

In a fully turbulent flow (\(\text {Re} > 10^5\)) in a pipe of diameter \(d\), for a constant pressure gradient, the dependence of volumetric flow rate of an incompressible fluid is

• \(d\)

• \(d^2\)

• \(d^{2.5}\)

• \(d^4\)

GATE-CH-2001-1-8-fm-1mark

Applying pressure drop across a capillary results in a volumetric flow rate \(Q\) under laminar flow conditions. The flow rate, for the same pressure drop, in a capillary of the same length but half the radius is

• \(Q/2\)

• \(Q/4\)

• \(Q/8\)

• \(Q/16\)

GATE-CH-2002-1-7-fm-1mark

For turbulent flow of an incompressible fluid through a pipe, the flow rate \(Q\) is proportional to \((\Delta P)^n\), where \(\Delta P\) is the pressure drop. The value of exponent \(n\) is

• 1

• 0

• \(<1\)

• \(>1\)

GATE-CH-2004-11-fm-1mark

The equivalent diameter for flow through a rectangular duct of width \(B\) and height \(H\) is

• \(\displaystyle \frac {HB}{2(H+B)}\)

• \(\displaystyle \frac {HB}{(H+B)} \)

• \(\displaystyle \frac {2HB}{(H+B)} \)

• \(\displaystyle \frac {4HB}{(H+B)} \)

GATE-CH-2008-10-fm-1mark

Losses for flow through valves and fittings are expressed in terms of

• drag coefficient

• equivalent length of a straight pipe

• shape factor

• roughness factor

GATE-CH-2010-22-fm-1mark

In Hagen-Poiseuille flow through a cylindrical tube, the radial profile of shear stress is

• constant

• cubic

• parabolic

• linear

GATE-CH-2012-10-fm-1mark

Water is flowing under laminar conditions in a pipe of length \(L\). If the diameter of the pipe is doubled, for a constant volumetric flow rate, the pressure drop across the pipe

• decreases 2 times

• decreases 16 times

• increases 2 times

• increases 16 times

GATE-CH-2013-13-fm-1mark

For a Newtonian fluid flowing in a circular pipe under steady state conditions in fully developed laminar flow, the Fanning friction factor is

• \(0.046\;\text {Re}^{-0.2}\)

• \(0.0014 + \dfrac {0.125}{{\text {Re}}^{0.32}}\)

• \(\dfrac {16}{\text {Re}}\)

• \(\dfrac {24}{\text {Re}}\)

GATE-CH-2014-12-fm-1mark

In case of a pressure driven laminar flow of a Newtonian fluid of viscosity (\(\mu \)) through a horizontal circular pipe, the velocity of the fluid is proportional to

• \(\mu \)

• \(\mu ^{0.5}\)

• \(\mu ^{-1}\)

• \(\mu ^{-0.5}\)

GATE-CH-2016-6-fm-1mark

For a flow through a smooth pipe, the Fanning friction factor (\(f\)) is given by \(f=m\text {Re}^{-0.2}\) in the turbulent flow regime, where \(\text {Re}\) is the Reynolds number and \(m\) is a constant. Water flowing through a section of this pipe with a velocity 1 m/s results in a frictional pressure drop of 10 kPa. What will be the pressure drop across this section (in kPa), when the velocity of water is 2 m/s?

• 11.5

• 20

• 34.8

• 40

GATE-CH-2017-36-fm-2mark

The following table provides four sets of Fanning friction factor data, for different values of Reynolds number (Re) and roughness factor \((k/D)\).

Which of the above sets of friction factor data is correct?

• Set I

• Set II

• Set III

• Set IV

GATE-ME-2013-A-7-fm-1mark

For steady, fully developed flow inside a straight pipe of diameter \(D\), neglecting gravity effects, the pressure drop \(\Delta P\) over a length \(L\) and the wall shear stress \(\tau _w\) are related by

• \(\tau _w=\dfrac {\Delta P D}{4L}\)

• \(\tau _w=\dfrac {\Delta P D^2}{4L^2}\)

• \(\tau _w=\dfrac {\Delta P D}{2L}\)

• \(\tau _w=\dfrac {4\Delta P L}{D}\)

GATE-XE-2012-B-6-fm-1mark

In the case of a fully developed flow through a pipe, the shear stress at the centerline is

• a function of the axial distance

• a function of the centerline velocity

• zero

• infinite

GATE-CH-2015-10-fm-1mark

Two different liquids are flowing through different pipes of the same diameter. In the first pipe, the flow is laminar with a centerline velocity, \(v_{\text {max},1}\), whereas in the second pipe, the flow is turbulent. For turbulent flow, the average velocity is 0.82 times the centerline velocity, \(v_{\text {max},2}\). For equal volumetric flow rates in both the pipes, the ratio \(v_{\text {max},1}/v_{\text {max},2}\) (up to two decimal places) is ____________

• Answer

GATE-XE-2015-B-13-fm-2mark

The figure shows a reducing area conduit carrying water. The pressure \(P\) and velocity \(V\) are uniform across sections 1 and 2. The density of water is 1000 kg/m³. If the total loss of head due to friction is just equal to the loss of potential head between the inlet and the outlet, then \(V_2\) in m/s will be ____________

• Answer

GATE-CH-1996-14-fm-5mark

Ammonia at atmospheric pressure and 300 K with a bulk stream velocity of 10 m/s flows in a pipe of i.d. 25 cm. Calculate: (i) the pressure drop per 100 m length (in N/m\(^2\)) of the pipe, and (ii) the power consumed (in W). Friction factor \(f = 0.079 \text {Re}^{-0.25}\) in the turbulent regime. Viscosity of ammonia may be taken as 10.2 \(\times 10^{-6}\) kg/(m.s).

(i) {#1}

(ii) {#2}

GATE-CH-2001-8-fm-5mark

The inlet velocity of water (\(\rho = 1000\) kg/m\(^3\)) in a right angled bend-reducer is \(v_1=1\) m/sec, as shown below. The inlet diameter is \(D_1=0.8\) m and the outlet diameter is \(D_2=0.4\) m. The flow is turbulent and the velocity profiles at the inlet and outlet are flat (plug flow). Gravitational forces are negligible.

(a) Find the pressure drop (\(P_1-P_2\)) across the bend assuming negligible friction losses, in kPa. {#1}

(b) If the actual pressure drop is (\(P_1-P_2\)) = 8.25 kPa, find the friction loss factor (\(K_f\)) based on the velocity \(v_1\). {#2}

GATE-CH-2003-51-fm-2mark

A centrifugal pump is used to pump water through a horizontal distance of 150 m and then raised to an overhead tank 10 m above. The pipe is smooth with an I.D. of 50 mm. What head (m of water) must the pump generate as its exit (E) to deliver water at a flow rate of 0.001 m³/s? The Fanning friction factor, \(f\) is 0.0062.

• 10 m

• 11 m

• 12 m

• 20 m

GATE-CH-2006-36-fm-2mark

A liquid is pumped at the flow rate \(Q\) through a pipe of length \(L\). The pressure drop of the fluid across the pipe is \(\Delta P\). Now a leak develops at the mid-point of the length of the pipe and the fluid leaks at the rate of \(Q/2\). Assuming that the friction factor in the pipe remains unchanged, the new pressure drop across the pipe for the same inlet flow rate (\(Q\)) will be

• \((1/2)\Delta P\)

• \((5/8)\Delta P\)

• \((3/4)\Delta P\)

• \(\Delta P\)

GATE-CH-2006-37-fm-2mark

In a laminar flow through a pipe of radius \(R\), the fraction of the total fluid flowing through a circular cross-section of radius \(R/2\) centered at the pipe axis is

• 3/8

• 7/16

• 1/2

• 3/4

GATE-CH-2009-30-fm-2mark

Two identical reservoirs, open at the top, are drained through pipes attached to the bottom of the tanks as shown below. The two drain pipes are of the same length, but of different diameters \((D_1>D_2)\). Assuming the flow to be steady and laminar in both drain pipes, if the volumetric flow rate in the larger pipe is 16 times of that in the smaller pipe, the ratio \(D_1/D_2\) is

• 2

• 4

• 8

• 16

GATE-CH-2011-34-fm-2mark

Two liquids (\(P\) and \(Q\)) having same viscosity are flowing through a double pipe heat exchanger as shown in the schematic below.

Densities of \(P\) and \(Q\) are 1000 and 800 kg/m³ respectively. The average velocities of the liquids \(P\) and \(Q\) are 1 and 2.5 m/s respectively. The inner diameters of the pipes are 0.31 and 0.1 m. Both pipes are 5 mm thick. The ratio of the Reynolds numbers Re\(_P\) to Re\(_Q\) is

• 2.5

• 1.55

• 1

• 4

GATE-CH-2011-36-fm-2mark

A liquid is flowing through the following pipe network. The length of pipe sections P, Q, R and S shown in the schematic are equal. The diameters of the sections P and R are equal and the diameter of the section Q is twice that of S. The flow is steady and laminar. Neglecting curvature and entrance effects, the ratio of the volumetric flow rate in the pipe section Q to that of S is

• 16

• 8

• 2

• 1

GATE-CH-1988-12-i-fm-6mark

What pressure drop per unit length (in Pa/m) is required in order to pump water at 25\(^\circ \)C through a pipe 5 cm in diameter at a rate of 68 cm\(^3\)/s? Viscosity of water at 25\(^\circ \)C is 1 cP.
____________

• Answer

GATE-CH-1989-12-ii-fm-5mark

Water is pumped from a tank \(A\) to \(B\) using a 5 cm diameter pipe and a pump with the delivery head of 30 m. Both the tanks are uncovered and the water level in the tank \(B\) is 20 m above the water level in the tank \(A\). The total pressure loss coefficient for the piping is 50. Calculate the velocity of water (in m/s) through the piping. Take \(g = 10\) m/s\(^2\).
____________

• Answer

GATE-CH-1990-12-i-fm-6mark

Nikuradse developed a semi theoretical correlation for \(f\) vs. Re for steady turbulent flow in smooth pipes (\(10^5 < \text {Re} < 10^7\)): \(1/\sqrt {f} = 1.75 \ln (\text {Re} \sqrt {f}) - 0.4\). Toluene (\(\rho \) = 866 kg/m\(^3\), \(\mu \) = 0.0008 N.s/m\(^2\)) is to be conveyed through a 100 m pipeline of diameter 0.2 m. What is the maximum flow rate of toluene in kg/s that can be maintained, if the frictional pressure loss is not to exceed 10 kN/m\(^2\)?
____________

• Answer

GATE-CH-1997-14-fm-5mark

In a delivery line for carbon tetrachloride at the constant flowrate of \(4\times 10^{-5}\) m\(^3\)/s, the first 1000 m long section is of 20 mm inside diameter smooth pipe followed by another 1000 m long section of 50 mm inside diameter smooth pipe, as shown in figure.

 
Estimate the pressure drop (in kPa) over the entire length of the delivery line. Neglect the minor losses due to sudden enlargement of pipe diameter.
For carbon tetrachloride, viscosity = \(10^{-3}\) Pa.s, and density = 1500 kg/m\(^3\)
For laminar flow, \(f=16/\text {Re}\)
For transitional–turbulent flow, \(f = 0.079 \text {Re}^{-0.25}\) where \(f\) is the Fanning friction factor.
____________

• Answer

GATE-CH-2000-7-fm-5mark

A hydrocarbon oil (viscosity 0.025 Pa.s and density 900 kg/m\(^3\)) is transported using a 0.6 m diameter, 10 km long pipe. The maximum allowable pressure drop across the pipe length is 1 MPa. Due to a maintenance schedule on this pipeline, it is required to use a 0.4 m diameter, 10 km long pipe to pump the oil at the same volumetric flow rate as in the previous case. Estimate the pressure drop for the 0.4 m diameter pipe (in MPa). Assume both pipes to be hydraulically smooth and in the range of operating conditions, the Fanning friction factor is given by: \(f = 0.079\text{Re}^{-0.25}\).

• Answer

GATE-CH-2013-32-fm-2mark

Water (density 1000 kg/m³) is flowing through a nozzle, as shown below and exiting to the atmosphere. The relationship between the diameters of the nozzle at locations 1 and 2 is \(D_1 = 4\;D_2\). The average velocity of the stream at location 2 is 16 m/s and the frictional loss between location 1 and location 2 is 10000 Pa. Assuming steady state and turbulent flow, the gauge pressure in Pa, at location 1 is ____________

• Answer

GATE-CH-2017-35-fm-2mark

Oil is being delivered at a steady flowrate through a circular pipe of radius \(1.25\times 10^{-2}\) m and length 10 m. The pressure drop across the pipe is 500 Pa. The shear stress at the pipe wall, rounded to 2 decimal places, is ____________Pa.

• Answer

GATE-CH-2008-39-fm-2mark

Match the following:

Group I	Group II
(P) Euler number	(1) Viscous force / Inertial force
(Q) Froude number	(2) Pressure force / Inertial force
(R) Weber number	(3) Inertial force / Gravitational force
	(4) Inertial force / Surface tension force

• P-1, Q-2, R-3

• P-2, Q-3, R-4

• P-3, Q-2, R-1

• P-4, Q-3, R-2