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Q.

A tube filled with water and closed at both ends uniformly rotates in a horizontal plane about the OO' axis. The manometers A and B fixed in the tube at distances r1 and r2 from rotational axis indicate pressure p1 and p2 , respectively. Determine the angular velocity ω of rotation of the tube.

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a

ω=2(p2−p1)ρ(r22−r12)

b

ω=2(p2−p1)ρ(r22+r12)

c

ω=2(r22−r12)p1−p2

d

ω=2(p2−p1)ρr1r2

answer is A.

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Detailed Solution

Consider the condition of equilibrium for the mass of water contained between cross section separated by x and x+dx from rotation axis.dp=ρω2xdx ; ∫p1p2dp=∫r1r2ρω2xdxp2−p1=ρω2[x22]r1r2=ρω2(r22−r122) ω=2ρ(p2−p1)(r22−r12)

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A tube filled with water and closed at both ends uniformly rotates in a horizontal plane about the OO' axis. The manometers A and B fixed in the tube at distances r1 and r2 from rotational axis indicate pressure p1 and p2 , respectively. Determine the angular velocity ω of rotation of the tube.