Equal volumes of two immiscible liquids of densities 2ρ and 4ρ are filled in a vessel as shown in figure. Two small holes are punched at depths h/2 and 2h from the surface of lighter liquid. If v₁ and v₂ are the velocities of efflux at these two holes, then v₂/v₁ is k. Find k².
Physics · Mixed Chapter
JEE Mains

Question

Equal volumes of two immiscible liquids of densities 2ρ and 4ρ are filled in a vessel as shown in figure. Two small holes are punched at depths h/2 and 2h from the surface of lighter liquid. If v₁ and v₂ are the velocities of efflux at these two holes, then v₂/v₁ is k. Find k².

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: At the upper hole, depth below the surface of the 2ρ liquid is h/2. Torricelli's law gives v₁²=2g(h/2)=gh. Step 2: The lower hole lies under h of density 2ρ plus h of density 4ρ, so gauge pressure there is Δp=(2ρ)gh+(4ρ)gh=6ρgh. Step 3: The exiting lower fluid has density 4ρ, giving v₂²=2Δp/(4ρ)=3gh. Step 4: (v₂/v₁)²=v₂²/v₁²=3. Thus k²=3.