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 B is twice that of in A . If the liquid mass flux through each hole is equal, then the ratio of the densities of the liquids respectively, is

Step-by-step solution

Let the velocity of liquid from hole in A is v₁ and velocity of liquid from hole in B is v₂ , then from equation of continuity aligned A₁ v₁ & =A₂ v₂ A v₁ & =2 A v₂ v₂ & = v₁ 2 aligned Volume of liquid coming out per second from hole in tank A=A₁ v₁=A v₁ Mass m₁=A v₁ ₁ Similarly, aligned m₂ & =A₂ v₂ ₂ & =2 A v₁ 2 ₂ & =A v₁ ₂ aligned But aligned & m₁=m₂ & A v₁ ₁=A v₁ ₂ & ₁ ₂ =1 & aligned