Fluid Properties and Manometry

 Question 1
The pressure in a pipe at $X$ is to be measured by an open manometer as shown in figure. Fluid $A$ is oil with a specific gravity of 0.8 and Fluid $B$ is mercury with a specific gravity of 13.6. The absolute pressure at $X$ is $\mathrm{kN} / \mathrm{m}^{2}$ (round off to one decimal place).
[Assume density of water as $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and acceleration due to gravity as $9.81 \mathrm{~m} / \mathrm{s}^{2}$ and atmospheric pressure as $\left.101.3 \mathrm{kN} / \mathrm{m}^{2}\right]$

 A 115.2 B 253.6 C 254.3 D 140.5
GATE CE 2023 SET-2   Fluid Mechanics and Hydraulics
Question 1 Explanation:

Equating pressure at $\mathrm{A}-\mathrm{A}^{\prime}$
\begin{aligned} & P_{a t m}+\rho_{B} \gamma_{w} \times \frac{25}{100}=P_{x}-\rho_{A} \gamma_{w} \times \frac{75}{100} \\ & \therefore \quad P_{x}=P_{a t m}+\rho_{B} \gamma_{w} \times 0.25+\rho_{A} \gamma_{w} 0.75 \end{aligned}
$\begin{gathered} =101.3+13.6 \times 9.81 \times 0.25+0.8 \times 9.81 \times 0.75 \\ =140.54 \mathrm{kN} / \mathrm{m}^{2} \end{gathered}$
 Question 2
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 2 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 3
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 3 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 4
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 5
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 5 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
$=20+0.74=20.74 \mathrm{cm}$

There are 5 questions to complete.