A cylindrical vessel of radius 0.30 m contains water and rotates about its vertical axis. The free surface at the rim is 45 cm higher than the free surface at the axis. Taking g = 10 m/s², the angular speed of rotation is N rad/s. Find N.
Physics · Fluid Mechanics · question based on variation of pressure
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Question

A cylindrical vessel of radius 0.30 m contains water and rotates about its vertical axis. The free surface at the rim is 45 cm higher than the free surface at the axis. Taking g = 10 m/s², the angular speed of rotation is N rad/s. Find N.

Physics · Fluid Mechanics · question based on variation of pressure

G1 Physics · Accepted Answer

For rigid-body rotation, Δh = ω²R²/(2g). Therefore, ω² = 2gΔh/R². Substitute g = 10 m/s², Δh = 0.45 m, R = 0.30 m. Thus, ω² = 2×10×0.45/0.30² = 9/0.09 = 100. Hence, ω = 10 rad/s. Therefore, N = 10.