Water rotates as a rigid body with angular speed 5 rad/s. Two points at the same height are located 0.20 m and 0.40 m from the rotation axis. The pressure difference between the outer and inner points is N Pa. Take ρ = 1000 kg/m³. Find N.
Physics · Fluid Mechanics · question based on variation of pressure
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Question

Water rotates as a rigid body with angular speed 5 rad/s. Two points at the same height are located 0.20 m and 0.40 m from the rotation axis. The pressure difference between the outer and inner points is N Pa. Take ρ = 1000 kg/m³. Find N.

Physics · Fluid Mechanics · question based on variation of pressure

G1 Physics · Accepted Answer

At the same height in a rotating liquid, P₂−P₁ = ρω²(r₂²−r₁²)/2. Substitute ρ = 1000 kg/m³, ω = 5 rad/s, r₁ = 0.20 m, r₂ = 0.40 m. Therefore, ΔP = 1000×25×(0.40²−0.20²)/2 = 1000×25×(0.16−0.04)/2 = 1500 Pa. Hence, N = 1500.