# Fluid Statics

 Question 1
A pressure measurement device fitted on the surface of a submarine, located at a depth H below the surface of an ocean, reads an absolute pressure of 4.2 MPa. The density of sea water is 1050 $kg/m^3$, the atmospheric pressure is 101 kPa, and the acceleration due to gravity is 9.8 $m/s^2$. The depth H is _______ m (round off to the nearest integer).
 A 128 B 398 C 478 D 256
GATE ME 2021 SET-1   Fluid Mechanics
Question 1 Explanation:

\begin{aligned} &P_{A}=4.2 \mathrm{MPa}\;\;\;\;\text { [Absolute pressure] }\\ P_{\text {atm }} &=101 \mathrm{kPa} \\ \rho &=1050 \mathrm{~kg} / \mathrm{m}^{3} \\ g &=9.8 \mathrm{~m} / \mathrm{s}^{2} \\ P_{A} &=P_{\text {atm }}+\rho \mathrm{gH} \\ 4.2 \times 10^{6} &=\left(101 \times 10^{3}\right)+[1050 \times 9.81 \times \mathrm{H}] \\ H &=397.94 \text { or } 398 \mathrm{~m} \end{aligned}
 Question 2
In the space above the mercury column in a barometer tube, the gauge pressure of the vapour is
 A positive, but more than one atmosphere B negative C zero D positive, but less than one atmosphere
GATE ME 2020 SET-2   Fluid Mechanics
Question 2 Explanation:

In space above mercury column in barometer, ideally perfect vaccum is expected. But due to evaporation of mercury , the pressure in that space is equal to vapour pressure of mercury [nearly 0.2 Pa (abs)] . As absolute pressure in that space is less than atmospheric pressure, gauge pressure is negative.

 Question 3
Which of the following conditions is used lo determine the stable equilibrium of all partially submerged floating bodies?
 A Centre of buoyancy must be above the centre of gravity B Centre of buoyancy must be below the centre of gravity C Metacentre must be at a higher level than the centre of gravity D Metacentre must be at a lower level than the centre of gravity
GATE ME 2020 SET-2   Fluid Mechanics
Question 3 Explanation:
Metacentre must be higher level than the centre of gravity
 Question 4
For the stability of a floating body the
 A centre of buoyancy must coincide with the centre of gravity B centre of buoyancy must be above the centre of gravity C centre of gravity must be above the centre of buoyancy D metacenter must be above the centre of gravity
GATE ME 2017 SET-2   Fluid Mechanics
Question 4 Explanation:

$GM=BM-BG$

(i) $GM \gt 0$, stable
(ii) $GM = 0$, Neutral
(iii) $GM \gt 0$, unstable

NOTE:: Metacentre (M) must always be above the centre of gravity.
 Question 5
Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions 2R x L at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius R. The tank is filled with a liquid of density $\rho$ up to the tip of the plug. The gravitational acceleration is g. Neglect the effect of the atmospheric pressure.

The force F required to hold the plug in its position
 A $2\rho R^{2}gL\left( 1-\frac{\pi }{4}\right )$ B $2\rho R^{2}gL\left( 1+\frac{\pi }{4}\right )$ C $\pi R^{2}\rho gL$ D $\frac{\pi }{2}\rho R^{2}gL$
GATE ME 2016 SET-2   Fluid Mechanics
Question 5 Explanation:

\begin{aligned} \text{Volume, } V_{total}&=2R \times L \times R\\ &=2R^2L\;\;...(i)\\ \text{Volume: }V_1&=\frac{1}{2}\times \pi R^2 \times L\;\;...(ii)\\ F&= \text{Weight of fluid}\\ &=[V_{total}-V_{1}]\rho g\\ &=\left [ 2R^2L-\frac{\pi R^2L}{2} \right ]\rho g\\ &=\left [ 1-\frac{\pi}{4} \right ]2R^2Lg\rho \\ &=2\rho R^2gL\left [ 1-\frac{\pi}{4} \right ] \end{aligned}

There are 5 questions to complete.

### 1 thought on “Fluid Statics”

1. ANSWER FOR QN:20 IS B
WHY BECAUSE IN MOHR’S CIRCLE DIAGRAM NORMAL STRESS IS POINTED ON NEGATIVE X-AXIS.