Flow Rate of Water with Pressure Difference

[Idea04]

Does water that encounters pressure difference or slight resistance have the same flow rate if there were no pressure difference's or resistance at all?

 

[quark]

If there is no pressure(head, rather) difference, there is no flow at all. Secondly, it depends upon the type of device that is pushing the fluid. There can be same flow with varying resistance but other factors will change (for ex. power)

 

[Andrew Mason]

Does water that encounters pressure difference or slight resistance have the same flow rate if there were no pressure difference's or resistance at all?

For flow in a pipe with no losses, the energy density is constant (Bernoulli's equation):

$$P + \rho gh + \frac{1}{2}\rho v^2 = \text{Constant}$$

So if there are energy losses in the pipe, what do you think will happen to pressure and speed (assume the pipe is level)?

AM

 

[Idea04]

well I'm talking about water flowing vertically downward through a pipe. Then enters upward through a larger column filled with water with a piston or weight on top pushing downward on the water. but the pressure in the larger column is lower than the pipe flowing downward. Would the flow entering the large column still be the same as it would be if there were no pressure pushing downward in the larger column?

 

[Andrew Mason]

well I'm talking about water flowing vertically downward through a pipe. Then enters upward through a larger column filled with water with a piston or weight on top pushing downward on the water. but the pressure in the larger column is lower than the pipe flowing downward. Would the flow entering the large column still be the same as it would be if there were no pressure pushing downward in the larger column?

No. If there were no weight pushing down in the large column, the water would move faster. Think about it in terms of energy. If the energy of the incoming water is not used in lifting the weight, what must be happening to the energy of the water in the large side? (Hint: apply Bernoulli's equation)

AM

 

[Idea04]

so if I'm to get this right the weight pushing down exerts pressure and will slow the amount of water entering the column. so when the column has less water in it, the flow rate would increase compared to if the column has a higher amount of water in it.

 

[Andrew Mason]

so if I'm to get this right the weight pushing down exerts pressure and will slow the amount of water entering the column. so when the column has less water in it, the flow rate would increase compared to if the column has a higher amount of water in it.

It is all about pressure. Water will flow from higher pressure to lower pressure.

The pressure on the top of the large column is mg/A where mg is the weight pushing down and A is the area of the column. If that pressure is less than the force/area pushing down on the thin column, water will flow into the large column and the weight will rise. If it is less, the water will flow out of the large column and the weight will lower.

The pressure at the bottom, where the thin column connects to the large column, is determined by the height of the water in each column. The pressure is $\rho gh$ where h is the height of the column of water. Water will move until the pressure difference at the bottom is 0.

AM

 

[Idea04]

Ok then. But if we reverse that flow and the weight lowers pushing the water out, Will the flow be the same even though the pressure drops with depth? Because wouldn't the weight always lower at a constant rate?

 

[Andrew Mason]

Ok then. But if we reverse that flow and the weight lowers pushing the water out, Will the flow be the same even though the pressure drops with depth? Because wouldn't the weight always lower at a constant rate?

Why? Analyse the forces on the weight. What is the force pushing it down? What is the force that opposes it? How do they compare?

AM