A closed tube filled with water is rotating uniformly in a horizontal plane about the axis O O ' as shown in the figure. The manometers A and B which are fixed on the tube at distances r 1 and r 2 , indicate pressures P 1 and P 2 respectively. The angular velocity ( ω ) of the tube is

Question

A closed tube filled with water is rotating uniformly in a horizontal plane about the axis O O ' as shown in the figure. The manometers A and B which are fixed on the tube at distances r 1 and r 2 , indicate pressures P 1 and P 2 respectively. The angular velocity ( ω ) of the tube is, ω = 2 P 2 - P 1 ρ r 2 2 - r 1 2, ω = 2 P 2 + P 1 ρ r 2 2 - r 1 2, ω = 2 P 2 + P 1 ρ r 2 2 + r 1 2, ω = 2 P 2 - P 1 ρ r 2 2 + r 1 2

MARKS App · Accepted Answer

Consider the condition of equilibrium for the mass of water contained between cross section separated by x and x + d x from rotation axis. d p = ρ ω 2 x d x ; ∫ p 1 p 2 d p = ∫ r 1 r 2 ρ ω 2 x d x p 2 - p 1 = ρ ω 2 x 2 2 r 1 r 2 = ρ ω 2 r 2 2 - r 1 2 2 ω = 2 P 2 - P 1 ρ r 2 2 - r 1 2

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