First slide

Fluid statics

Question

Tanks A and B open at the top contain two different liquids upto certain height in them. A hole is made to the wall of each tank at a depth 'h' from the surface of the liquid. The area of the hole in A is twice that of in B. If the liquid mass flux through each hole is equal, then the ratio of the densities of the liquidsrespectively, is

Easy

A

2/1
B

3/2
C

2/3
D

1/2

Solution

By Toricelli's equaiton velocity of efflux $\large u=\sqrt {2gh}$ . If 'a' be the area of hole, then a_A = 2.a_BMass flow rate is $\large \rho_A.a_A.u=\rho_B.a_B.u$
$\large \Rightarrow \rho_A.(2a_B)=\rho_B.a_B$
$\large \Rightarrow \frac {\rho_A}{\rho_B}=\frac 12$

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