Question

A manometer consists of a U-shaped tube containing water. One side is connected to the apparatus and the other side is open to the atmosphere. If external pressure is $1atm$ and the level of water on the open side of the tube is $10cm$ lower than the side connected to the apparatus. The pressure of gas is (Assume density of water is $1g/ml$ and $g$ is $10m/{s^2}$.$1atm = 1.013 \times {10^5}Pa$).

Answer 1

Hint: We have to know that in a U-tube manometer, the pressure distinction across each end is adequate to the pressure thanks to height difference within the liquid at both ends with additional pressure at the top wherever the liquid has raised.
\[{p_2} - {p_1} = \rho \times g \times h\]
Where,
\[{P_1}\] is the pressure of the liquid on the where the liquid has risen
The pressure of the liquid on the opposite half is ${P_2}$
The density of the liquid of the liquid is $\rho $
The acceleration due to gravity is g.
The peak difference at both ends is h.

Complete step by step solution:
Given,
The atmospheric pressure is $1.013 \times {10^5}Pa$.
The density of the water is $1g/ml$.
The acceleration due to gravity g is $10m/{s^2}$.
The peak difference at both ends is h is $10cm = 0.10m$.
Let us substitute the values in the equation,
${p_2} = {p_1} + \rho \times g \times h$
Now we substitute the known values we get,
\[ \Rightarrow {p_2} = 1.013 \times {10^5} + 1 \times 10 \times 0.10\]
On simplifying we get,
\[ \Rightarrow {p_2} = 1.013 \times {10^5}Pa\]
The pressure of gas is $1.013 \times {10^5}Pa$.

Note:
We must remember that the static pressure is standardized all told directions, so pressure measurements are freelance of direction in an immoveable (static) fluid. Flow, though, applies additional pressure on surfaces vertical to the flow direction, while having very little impact on surfaces parallel to the flow direction. This directional element of pressure in an exceedingly moving fluid called dynamic pressure. Associate instrument opposite the flow direction events the insert of the static and dynamic pressures; this activity is called the full pressure or stagnation pressure. Since dynamic pressure is recognized to static pressure, it's neither gauge nor absolute; it is a degree of distinction pressure. Whereas static gauge pressure is of main significance to deciding web a whole lot on pipe walls, dynamic pressure is functioning to measure flow rates and airspeed.