Water flows through a smooth stationary 90° pipe bend at a constant mass rate 2 kg/s. Its speed is 10 m/s before and after the bend. Initially the velocity is along +x, and after the bend it is along +y. Neglect pressure-force differences and gravity. If the magnitude of the force exerted by water on the pipe is N√2 newton, find N.
Physics · Center of maas , Momentum and Collision · variable mass system
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Question

Water flows through a smooth stationary 90° pipe bend at a constant mass rate 2 kg/s. Its speed is 10 m/s before and after the bend. Initially the velocity is along +x, and after the bend it is along +y. Neglect pressure-force differences and gravity. If the magnitude of the force exerted by water on the pipe is N√2 newton, find N.

Physics · Center of maas , Momentum and Collision · variable mass system

G1 Physics · Accepted Answer

The force required to change the water momentum is the rate of momentum change: F(on water) = (dm/dt)[v(out) − v(in)]. Here, v(in) = (10,0) m/s, v(out) = (0,10) m/s, dm/dt = 2 kg/s. Therefore F(on water) = 2[(0,10) − (10,0)] = 2(−10,10) = (−20,20) N. Magnitude: |F| = √(20²+20²) = 20√2 N. The force exerted by water on the pipe is equal and opposite, with the same magnitude. Thus N = 20.