Fluid Mechanics -Momentum Equation

In summary, the conversation is about using a weigh tank to calibrate a flow meter by measuring weights as a function of time. Water is entering the tank at a speed of 20 ft/s through a 1.5 in. diameter pipe. The question is to determine the scale reading after 10 seconds, with the empty tank weighing 50 lbf. The original answer was 74.8 lbf but the correct answer is 212.67 lbf. After further discussion, it is determined that the mistake was in not considering the change in momentum of the water and not including the gc factor in the calculation of the weight of water. The momentum of the falling water is already included in the momentum equation.
  • #1
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Fluid Mechanics --Momentum Equation

Homework Statement


A large weigh tank is to be used in the calibration of a flow metre. Measurements of weights as a function of time are to be made. Water enters the tank vertically from the flow metering system at a speed of 20 ft/s through a 1.5 in. diameter pipe. If the weight of the empty tank is 50 lbf, determine the scale reading at t=10 s.

I found the reading to be 74.8 lbf but the answer is 212.67 lbf.

Any help is appreciated.

The link to my working.

https://skydrive.live.com/?sc=photos&cid=6b041751c72e14ad#cid=6B041751C72E14AD&id=6B041751C72E14AD%21173
 
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  • #2


I am unable to decipher your link. Without considering the change in momentum of the water, I get about 203 pounds. If the pipe discharges vertically downward, you'll have to consider momentum change of the water adding to the weight of the vessel.
 
  • #3


Thanks for the reply.
I have already solved the question. Turned out there's a mistake when I calculated
the weight of water after 10 seconds and I did not include the gc factor. And yes,
momentum of the falling water is already included in the momentum equation.
 

1. What is the momentum equation in fluid mechanics?

The momentum equation in fluid mechanics is a fundamental equation that describes the relationship between the forces acting on a fluid and its resulting motion. It is based on the principle of conservation of momentum, which states that the total momentum of a closed system remains constant.

2. How is the momentum equation derived?

The momentum equation is derived from Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. By applying this law to a small volume of fluid, we can derive the momentum equation by considering the forces acting on the fluid, such as pressure, gravity, and viscous forces.

3. What is the significance of the momentum equation in fluid mechanics?

The momentum equation is essential in understanding and predicting the behavior of fluids in various applications, such as in aerodynamics, hydrodynamics, and fluid flow in pipes and channels. It allows us to calculate the forces and pressures acting on a fluid, as well as the resulting motion of the fluid.

4. Can the momentum equation be simplified?

Yes, the momentum equation can be simplified in certain cases, such as when the fluid is incompressible or when there is no external force acting on the fluid. In these cases, the momentum equation reduces to the well-known Bernoulli's equation, which is commonly used in fluid mechanics calculations.

5. How is the momentum equation applied in real-life situations?

The momentum equation is applied in various real-life situations, including the design of airplanes and cars, the flow of water in pipes, and the analysis of ocean currents. It is also used in industrial processes, such as in chemical reactors and pumps, to calculate the forces and motion of fluids.

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