Water flows through the pipe section shown. At the inlet the water velocity is 3.1 m/s and the mass flow rate is 12 kg/s. At the outlet the water velocity is 6.6 m/s. Determine the total nett force (Fbolts shown) exerted on the bolts holding the pipe together (not the force of each individual bolt). Provide answers to 1 decimal place and SI units are required
Question
Water flows through the pipe section shown. At the inlet the water velocity is 3.1 m/s and the mass flow rate is 12 kg/s. At the outlet the water velocity is 6.6 m/s.
Determine the total nett force (Fbolts shown) exerted on the bolts holding the pipe together (not the force of each individual bolt).
Provide answers to 1 decimal place and SI units are required
Solution
To solve this problem, we need to use the principle of conservation of momentum. The force exerted on the bolts is equal to the change in momentum of the water per unit time.
The momentum of the water at the inlet is given by the product of the mass flow rate and the velocity at the inlet. Similarly, the momentum of the water at the outlet is given by the product of the mass flow rate and the velocity at the outlet.
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Calculate the momentum at the inlet: Momentum_inlet = mass flow rate * velocity_inlet Momentum_inlet = 12 kg/s * 3.1 m/s = 37.2 kg*m/s
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Calculate the momentum at the outlet: Momentum_outlet = mass flow rate * velocity_outlet Momentum_outlet = 12 kg/s * 6.6 m/s = 79.2 kg*m/s
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The total force exerted on the bolts is equal to the change in momentum per unit time, which is the difference in momentum at the outlet and the inlet:
F_bolts = Momentum_outlet - Momentum_inlet F_bolts = 79.2 kgm/s - 37.2 kgm/s = 42.0 kg*m/s
So, the total force exerted on the bolts is 42.0 N.
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