The Pitot tube shown in the figure is used to measure fluid flow velocity in a pipe of cross sectional area $S$. It was invented by a French engineer Henri Pitot in the early $18^{th}$ century. The volume of the gas flowing across the section of the pipe per unit time is (The difference in the liquid columns is $\Delta h, \rho_0$ and $\rho$ are the densities of liquid and the gas respectively) :-
Diffcult
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Applying Bernoulli's theorem
$P _{ A }= P _{ B }+\frac{1}{2} \rho v ^2 \text { as, } v _{ A }=0$
$\frac{1}{2} \rho v^2=P_A-P_B=\Delta h_0 g$
So, $v=\sqrt{\frac{2 \Delta h \rho_0 g}{\rho}}$
Thus, rate of flow of gas, $Q = Sv = S \sqrt{\frac{2 \Delta h \rho g }{\rho}}$
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