# Fluid Properties and Manometry

 Question 1
A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids (S1, S2) are given in the figure.

The gauge pressure value (in $kN/m^{2}$, up to two decimal places) of $p_{1}$ is ______
 A -8.73 B -4.78 C -2.54 D 0
GATE CE 2018 SET-2   Fluid Mechanics and Hydraulics
Question 1 Explanation:

Taking $P_{1}$ is in gauge pressure.
\begin{aligned} P_{A}=& P_{1}+\left(0.88 \times 10^{3}\right) \cdot(9.81)(0.5) \\ &+\left(0.95 \times 10^{3}\right)(9.81)(1) \\ \left(10^{3}\right)(9.81)(0.5)=& P_{1}+\left(0.88 \times 10^{3}\right) \cdot(9.81)(0.5) \\ &+\left(0.95 \times 10^{3}\right)(9.81)(1) \\ P_{1}=&-8.73 \mathrm{kN} / \mathrm{m}^{2} \end{aligned}
 Question 2
A closed tank contains 0.5 m thick layer of mercury (specific gravity = 13.6) at the bottom. A 2.0 m thick layer of water lies above the mercury layer. A 3.0 m thick layer of oil (specific gravity = 0.6) lies above the water layer. The space above the oil layer contains air under pressure. The gauge pressure at the bottom of the tank is 196.2 kN/$m^{2}$. The density of water is 1000 kg/$m^{3}$ and the acceleration due to gravity is 9.81 m/$s^{2}$. The value of pressure in the air space is
 A 92.214 kN/$m^{2}$ B 95.644 kN/$m^{2}$ C 98.922 kN/$m^{2}$ D 99.321 kN/$m^{2}$
GATE CE 2018 SET-1   Fluid Mechanics and Hydraulics
Question 2 Explanation:

\begin{aligned} &P_{a i t} \text { is in gauge pressure. }\\ &\begin{array}{l} P_{a i r}+\left(0.6 \times 10^{3}\right)(9.81)(3)+\left(10^{3}\right)(9.81)(2) \\ \quad+\left(13.6 \times 10^{3}\right)(9.81)(0.5)=196.2 \times 10^{3} \\ P_{a i r}=92.214 \mathrm{kN} / \mathrm{m}^{2} \end{array} \end{aligned}
 Question 3
Bernoulli's equation is applicable for
 A viscous and compressible fluid flow B inviscid and compressible fluid flow C inviscid and incompressible fluid flow D viscous and incompressible fluid flow
GATE CE 2018 SET-1   Fluid Mechanics and Hydraulics
 Question 4
The figure shows a U-tube having a 5 mmx5 mm square cross-section filled with mercury (specific gravity = 13.6) up to a height of 20 cm in each limb (open to the atmosphere).

If 5 $cm^{3}$ of water is added to the right limb, the new height (in cm, up to two decimal places) of mercury in the LEFT limb will be_____
 A 1.73 B 19.26 C 20.74 D 2.73
GATE CE 2017 SET-2   Fluid Mechanics and Hydraulics
Question 4 Explanation:

\begin{aligned} P_{A} &=P_{B} \\ \left(13.6 \times 10^{3}\right) g \times(2 x) &=\left(10^{3}\right) g(20) \\ x &=\frac{10}{3.6}=0.735 \mathrm{cm} \end{aligned}
So, the new height (in cm to two decimal place of
mercury in the left limb will be
$=20+0.74=20.74 \mathrm{cm}$
 Question 5
Group I contains the types of fluids while Group II contains the shear stress - rate of shear relationship of different types of fluids, as shown in the figure.

The Correct match between Group I and Group II is
 A P-2, Q-4, R-1, S-5 B P-2, Q-5, R-4, S-1 C P-2, Q-4, R-5, S-3 D P-2, Q-1, R-3, S-4
GATE CE 2016 SET-2   Fluid Mechanics and Hydraulics
 Question 6
Three rigid buckets, shown as in the figures (1), (2) and (3), are of identical heights and base areas. Further, assume that each of these buckets have negligible mass and are full of water. The weights of water in these buckets are denoted as $W_{1},W_{2}, \; and \; W_{3}$ respectively. Also, let the force of water on the base of the bucket be denoted as $F_{1},F_{2}, \;and \; F_{3}$ respectively. The option giving an accurate description of the system physics is
 A $W_{2}=W_{1}=W_{3}\; and\; F_{2} \gt F_{1} \gt F_{3}$ B $W_{2} \gt W_{1} \gt W_{3}\; and\; F_{2} \gt F_{1} \gt F_{3}$ C $W_{2}=W_{1}=W_{3}\; and\; F_{1}=F_{2}=F_{3}$ D $W_{2} \gt W_{1} \gt W_{3}\; and \; F_{1}=F_{2}=F_{3}$
GATE CE 2014 SET-1   Fluid Mechanics and Hydraulics
Question 6 Explanation:
Bucket $\rightarrow$ identical height
$\rightarrow$ identical base area

$W_{2}>W_{1}>W_{3}$
Force on the base in each case will be equal
$to=\gamma_{w} h A$
Hence, $F_{1}=F_{2}=F_{3}$
 Question 7
The dimension for kinematic viscosity is
 A $\frac{L}{MT}$ B $\frac{L}{T^{2}}$ C $\frac{L^{2}}{T}$ D $\frac{ML}{T}$
GATE CE 2014 SET-1   Fluid Mechanics and Hydraulics
Question 7 Explanation:
The Sl unit of kinematic viscosity is $\mathrm{m}^{2} / \mathrm{s}$
Dimension of kinematic viscosity $[\mathrm{v}]=\mathrm{L}^{2} / \mathrm{T}$
 Question 8
In the inclined manometer shown in the figure below, the reservoir is large. Its surface may be assumed to remain at a fixed elevation. A is connected to a gas pipeline and the deflection noted on the inclined glass tube is 100 mm. Assuming $\theta =30^{\circ}$ and the manometric fluid as oil with specific gravity of 0.86, the pressure at A is
 A 43 mm water (vaccum) B 43 mm water C 86 mm water D 100 mm water
GATE CE 2004   Fluid Mechanics and Hydraulics
Question 8 Explanation:
Total pressure at A will be equal to the pressure at the surface of manometric fluid because above the surface, the gas pipeline is connected.
$\therefore$ Pressure at $A=100 \sin 30^{\circ} \mathrm{mm}$ of oil
$=50 \mathrm{mm} \text { of oil }$
We know that
\begin{aligned} S_{1} h_{1} &=S_{2} h_{2} \\ \Rightarrow \quad 0.86 \times 50 &=1 \times h_{2} \\ \Rightarrow &=43 \mathrm{mm} \text { of water } \end{aligned}
 Question 9
Two pipelines, one carrying oil (mass density 900 kg/$m^{3}$) and the other water, are connected to a manometer as shown in figure. By what amount the pressure in the water pipe should be increased so that the mercury levels in both the limbs of the manometer become equal ? (mass density of mercury= 13550 kg/$m^{3}$ and g = 9.81 m/$s^{2}$)
 A 24.7 kPa B 26.5 kPa C 26.7 kPa D 28.9 kPa
GATE CE 2003   Fluid Mechanics and Hydraulics
Question 9 Explanation:
Initially the pressure difference between water and oil can be given as

\begin{aligned} p_{w}+(1000 &\times 9.81 \times 1.5)+(13550 \times 9.81 \times 20 \\ \left.\times 10^{-2}\right)-(900 &\times 9.81 \times 3)=p_{0}\\ \Rightarrow \; p_{w t}+14715+26585.1-26487=p_{0} \\ \Rightarrow \quad p_{0}-p_{w}&=14813.1 \\ \Rightarrow \quad P_{0}-P_{w}&=14.8 \mathrm{kPa} &\ldots(i) \end{aligned}
To make the same level of mercury in both the limbs, the level of mercury should be decreased by 10 cm in right limb and increased by 10cm in lett limb
\begin{aligned} P_{w t}+(1000 \times 9.81 &\times 1.6)-(900 \times 9.81 \times 2.9)=p_{0}\\ \Rightarrow \quad P_{0}-p_{w t}&=-9.9 \mathrm{kPa} &\ldots(ii)\\ \end{aligned}
Subtracting (ii) from (i) we get
$\begin{array}{l} P_{W}-P_{N}=14.8+99 \\ P_{\mathrm{w} t}-P_{\mathrm{w}}=24.7 \mathrm{kPa} \text { (increase) } \end{array}$
There are 9 questions to complete.