Match
the following for a centrifugal pump with impeller speed n
P Capacity (1) proportional to n
Q Head (2) proportional to n2
(3)
proportional to n3
(A) P-2, Q-1
(B) P-1, Q-3
(C) P-2, Q-3
(D) P-1, Q-2
GATE
2006
Answer: (D)
The
magnitude of the force (in N) required to hold a body of volume 0.05 m3
and mass 40 kg in water (density 1000 kg/m3) at a depth of 0.1 m is
(g = 9.81 m/s2)
(A) Zero
(B) 98.1
(C) 490.5
(D) 882.9
GATE
2006
Answer: (B)
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 ΔP. 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
(A) (1/2) ΔP
(B) (5/8) ΔP
(C) (3/4) ΔP
(D) ΔP
GATE
2006
Answer: (B)
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
(A) 3/8
(B) 7/16
(C) 1/2
(D) ¾
GATE
2006
Answer: (B)
A
fluid obeying the constitutive equation
is held between two parallel plates a distance d apart. If the stress applied to the top plate is 3τ0, then the velocity with which the top plate moves relative to the bottom plate would be
GATE
2006
Answer: (C)
A
bed fluidized by water is used for cleaning sand contaminated with salt. The
particles of sand and salt have the same shape and size but different densities
(ρsand = 2500 kg/m3 and ρsalt = 2000 kg/m3). If the initial
volume fraction of the salt in the mixture is 0.3 and if the initial value of
the minimum fluidization velocity (Umf) is 0.9 m/s, find the final
value of the Umf (in m/s) when the sand is washed free of the salt
Assume that the bed characteristics (bed porosity and solid surface area per
unit volume) do not change during the operation and that the pressure drop per
unit length is directly proportional to the fluid velocity
(A) 0.70
(B) 0.90
(C) 1.00
(D) 1.46
GATE
2006
Answer: (C)
Two
spherical particles have the same outer diameter but are made of different
materials The first one (with material density ρ1) is solid, whereas
the second (with material density ρ2) is a hollow sphere with the
inner shell diameter equal to half the outer diameter. If both the spheres have
the same terminal velocity in any fluid, then the ratio of their material
densities, ρ2/ρ1, is
(A) 1
(B) 8/7
(C) 2
(D) 8
GATE
2006
Answer: (B)
The
mixing of rubber latex solution was studied in an unbaffled mixer in the
laboratory. The mixer was equipped with a six blade turbine impeller. A tyre
company scales this process up using a baffled tank. The baffled tank has 3
times the diameter of the lab scale mixer. It uses the same type of impeller
operated at the same speed. The relevant shape factors are also the same.
Assuming that laminar conditions prevail in both cases, the power requirement
in the industrial scale mixer
(A) is
3 times that of the lab scale mixer
(B) is
9 times that of the lab scale mixer
(C) is
27 times that of the lab scale mixer
(D) cannot
be estimated reliably due to the presence of baffles
GATE 2006
Answer: (C)
Let
dh be the hydrodynamic entrance length for mercury in laminar flow
in a pipe under isothermal conditions. Let dt, be its thermal
entrance length under fully developed hydrodynamic conditions. Which ONE of the
following is TRUE?
(A) dh
> dt
(B) dh
< dt
(C) dh
= dt
(D) dh
< dt only if the pipe is
vertical
GATE
2006
Answer: (A)
The
Boussinesq approximation for the fluid density in the gravitational force term
is given by ONE of the following (ρref is the fluid density at the
reference temperature Tref, and β is the thermal coefficient of
volume expansion at Tref)
(A)
ρ = ρref + Tref
β(ρ - ρref)
(B)
ρ = ρref - Tref
β(ρ - ρref)
(C)
ρ = ρref - Tref
β(T - Tref)
(D)
ρ = ρref - Tref (ρ
- ρref)+ ρref(T - Tref)/ Tref
GATE
2006
Answer: (C)
If the frequency
of the stirrer in a mixing tank is increased by a factor of 2 while all other
parameters are kept constant, by what factor is the power requirement increased
at high Reynolds number?
(A)
4
(B)
8
(C)
16
(D)
32
GATE
2005
Answer: (B)
Match
the following types of fluid (in group I) with their respective constitutive
relations (in group II), where τ is the stress and ϒ is the strain rate
(A)
P-I, Q-IV
(B)
P-IV, B-I
(C)
P-II, Q-III
(D)
P-III, Q-II
GATE
2005
Answer: (D)
For turbulent
flow past a flat plate, when no form drag is present, the friction factor and
the Chilton-colburn factor JD are related as
(A)
f and JD cannot be related
(B)
f is equal to JD
(C)
f is greater than JD
(D)
f is less than JD
GATE
2005
Answer: (C)
A dam of width
50 m is used to hold water in a reservoir. If the water height is 10 m from the
bottom of the dam, what is the total force F acting on the dam due to the
water? Assume g = 10 m/s2 and the fluid density is 1000 kg/m3
(A)
F = 12.5×106 N
(B)
F = 25×106 N
(C)
F = 50×106 N
(D)
F = 5×106 N
GATE
2005
Answer: (B)
The relation
between the stress and the strain rate (dux/dy) for the rapid flow
of granular material is given by τ = B (dux/dy)2 where B
is a constant. If M, L, and T are the mass, length and time dimension
respectively, what is the dimension of the constant B?
(A)
ML-1T-1
(B)
ML-2T-2
(C)
MT-1
(D)
ML-1
GATE
2005
Answer: (D)
Common statement for the next two
questions
Two
tanks A and B of cross sectional area 1 m2 each, contain a fluid of
density 1000 kg/m3 and viscosity 1 kg/(m.S). The tanks are connected
by a pipe of diameter 0.02 m and length 1 m, and check valve at the bottom.
Assume that the flow is laminar and there is no friction in the check valve. In
the initial state, the height of the fluid in the tank A is 6 m and the height
of the fluid in tank B is 2 m (as shown in the figure below). The check valve
is opened and the fluid flows from tank A to tank B till the levels in the two
tanks are equal in the final state. Assume g = 10 m/s2 in the
calculations.
What is the
average fluid velocity in the pipe as soon as the valve is opened?
(A)
0.25 m/s
(B)
0.5 m/s
(C)
1 m/s
(D)
2 m/s
GATE
2005
Answer: (B)
What is the
total energy loss between the initial and final states due to the fluid flow?
(A)
2×104 J
(B)
16×104 J
(C)
8×104 J
(D)
4×104 J
GATE
2005
Answer: (D)
What is terminal
velocity in m/s, calculated from stokes law for a particle of diameter 0.1×10-3
m, density 2800 kg/m3 settling in water of density 1000 kg/m3
and viscosity 10-3 kg/(m.s)? (Assume g =10 m/s2)
(A)
2×10-2
(B)
4×10-3
(C)
10-2
(D)
8×10-3
GATE
2005
Answer: (C)
Common statement for the next two
questions
A balloon of mass 0.01 kg is charged with
hydrogen to a pressure of 102 KPa and released from the ground level. During
its noise the hydrogen is permitted to escape from the balloon in order to
maintain a constant differential pressure of 2 KPa under which condition the
diameter of the balloon remains at 0.4 m. As this balloon rises it is assumed
that the temperature in and around the balloon remains constant at 273 K.
Further, the inertia of the balloon and the air resistance due to the rising
balloon may be neglected. Assume that the density of air at 273 K is 1.2733
kg/m3, the average molecular weight of air is 28.9, the atmospheric
pressure is 100 KPa and the acceleration due to gravity is 10 m/s2.
Select the correct value of the upward thrust (in N)
expressed in terms of outside pressure P which is expressed in Pa
(A)
10.06×107
P – 0.0122
(B)
3.97×10-6
P – 0.1006
(C)
15.03×10-7
P – 0.0534
(D)
8.08×10-6
P – 0.1362
GATE
2005
Answer: (B)
Select the value of the outside pressure P in Pa for
which there will be no force on the balloon?
(A)
25340
(B)
35530
(C)
12130
(D)
16860
GATE
2005
Answer: (A)
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