Question

In an air flow the velocity is measured by a Pitot tube (coefficient = 1.0). The mass density of air can be taken as $1.2kg/m^3$. If the head difference in a vertical U-tube holding water is 12 mm, then what is the velocity of air in m/s?

• A. 10
• B. 14
• C. 17
• D. 20

Answer 1

The correct option is B 14

(b)
We know that if $h_{1}and{h}_2$ are heights of the columns of liquids of mass density ${\rho }_{1}and{\rho }_2$ required to develop the same pressure p, at any point, then

$p={\rho }_1{h}_1={\rho }_2{h}_2$

${\rho }_1=1.2kg/m^3$

${\rho }_2=1000kg/m^3$

$h_2=12mm$

$h_1=?$

$\Rightarrow 1.2\times h_1=1000\times 12$

$\therefore h_1=10m$

$V_o=C\sqrt{2g{h}_1}$

$=1\times \sqrt{2\times 9.81\times 10}=14m/s$
Alternatively,

$V_o=C\sqrt{2gx(\frac{S_m}{S}-1)}$

$=\sqrt{2\times 9.8\times 12\times {10}^{-3}\times (\frac{1}{1.2\times {10}^{-3}}-1)}$

$=13.998\approx 14m/s$