1
GATE ME 2024
Numerical
+2
-1.33

A liquid fills a horizontal capillary tube whose one end is dipped in a large pool of the liquid. Experiments show that the distance $L$ travelled by the liquid meniscus inside the capillary in time $t$ is given by

$L = k \gamma^a R^b \mu^c \sqrt{t},$

where $\gamma$ is the surface tension, $R$ is the inner radius of the capillary, and $\mu$ is the dynamic viscosity of the liquid. If $k$ is a dimensionless constant, then the exponent $a$ is _______ (rounded off to 1 decimal place).

2
GATE ME 2016 Set 2
Numerical
+2
-0
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $$50$$ $$mm$$). The top plate is sliding parallel to the stationary bottom plate at a speed of $$3$$ $$m/s.$$ The flow between the plates is solely due to the motion of the top plate. The force per unit area (magnitude) required to maintain the bottom plate stationary is _______________ $$N/{m^2}.$$

Viscosity of the fluid $$\mu = 0.44\,\,kg/m$$-$$s$$ and density $$\rho = 888$$ $$kg/{m^3}.$$

3
GATE ME 2015 Set 3
+2
-0.6
Which of the following statement are TRUE, when the cavitation parameter $$\sigma = 0?$$
(i) The local pressure is reduced to vapor pressure.
(ii) Cavitation starts
(iii) Boiling of liquid starts
(iv) Cavitations stops

A
$$(i), (ii)$$ and $$(iv)$$
B
only $$(ii)$$ and $$(iii)$$
C
only $$(i)$$ and $$(iii)$$
D
$$(i),(ii)$$ and $$(iii)$$
4
GATE ME 2014 Set 1
Numerical
+2
-0
In a simple concentric shaft-bearing arrangement, the lubricant flows in the $$2$$ $$mm$$ gap between the shaft and the bearing. The flow may be assumed to be a plane Couette flow with zero pressure gradient. The diameter of the shaft is $$100$$ $$mm$$ and its tangential speed is $$10$$ $$m/s.$$ The dynamic viscosity of the lubricant is $$0.1$$ $$kg/m.s.$$ The frictional resisting force (in newton) per $$100$$ $$mm$$ length of the bearing is ______________.