Question

The arrangement shown in the figure measures the velocity V of a gas density
1 kg/$m^3$ flowing through a pipe. The acceleration due to gravity is 9.81 m/ $s^2$. If the manometric fluid is water (density 1000 kg/$m^3$) and the velocity V is 20 m/s, the differential head h (in mm) between the two arms of the manometer is____________

• A. 20.4

Answer 1

The correct option is A 20.4
Method :(i)

Given data: ${\rho }_{gas}=1kg/m^3;g=9.81m/s^2,$
${\rho }_m=1000kg/m^3,V=20m/s$

$Dynamicpressureofgas=(\rho gh{)}_{water}$

$\frac{1}{2}{\rho }_{gas}{V}^2={\rho }_m\times 9.81\times h$

$\frac{1}{2}\times 1\times (20{)}^2=1000\times 9.81\times h$

or h = 0.02038 m of water
= 20.38 mm of water

Method : (ii)

${\rho }_m=1000kg/m^3,{\rho }_{gas}=1kg/m^3$
V=20 m/s

$V=\sqrt{2gh(\frac{{\rho }_m}{{\rho }_{gas}}-1)}$

$20=\sqrt{2\times 9.81\times h(\frac{1000}{1}-1)}$

or h=20.40 mm of water