Speed and pressure relative to a piston (fluids)

[Mike Dacre]

I am studying for the MCAT and I got an interesting question from a Kaplan book:

15. A water tower operator is interested in increasing the pressure of a column of water that is applied to a piston. She hopes that increasing the pressure will increase the force being applied to the piston. The only way to increase the pressure is to alter the speed of the water as it flows through the pipe to the piston. How should the speed of the water be changed to increase the pressure and force?

• A. Increase the speed
• B. Decrease the speed
• C. Release water intermittently against the pipe
• D. The speed of water will not change pressure at the piston.

Correct Answer: B

Explanation:

This is a basic interpretation of Bernoulli's equation that states, at equal heights, speed and pressure of a fluid are inversely related (the Venturi effect). Decreasing the speed of the water will therefore increase its pressure. An increase in pressure over a given area will result in increased force being transmitted to the piston.​

This one is interesting to me, because I was sure the answer they wanted was B, because MCAT examiners and book writers love the relationship between velocity and pressure. I am very aware of the inverse relationship between speed and pressure in fluids.

However, I don't like this question, because of the fact that water operating a piston is going to push directly on the piston, and it is going to dramatically lose velocity as the kinetic energy is converted to work on the piston:

So in this case, I feel like the speed of the water would not have a dramatic effect on the pressure at the piston, for the simple reason that the speed at the piston will be determined by how fast the piston is moving, not how fast the water was released. I feel like if the only thing that can be varied is the initial speed of the fluid, and the fluid will almost stop, the only effect on pressure at the piston will be the mass of the fluid itself. Is my intuition on this flawed, is it the case that releasing the water much faster will result in a lower final pressure on the piston?

Possibly the issue here is that I am thinking about the final pressure, not the instantaneous pressure the moment the fluid touches the piston. Obviously, at the moment it touches the piston, the fluid would have a lower pressure that the same fluid moving slower, but this is a dumb comparison because if the fluid were moving slower there would be less of it in that instant anyway.

 

[Mike Dacre]

The Khan Acadamy seems to back me up here:

The idea that regions where the fluid is moving fast will have lower pressure can seem strange. Surely, a fast moving fluid that strikes you must apply more pressure to your body than a slow moving fluid, right? Yes, that is right. But we're talking about two different pressures now. The pressure that Bernoulli's principle is referring to is the internal fluid pressure that would be exerted in all directions during the flow, including on the sides of the pipe. This is different from the pressure a fluid will exert on you if you get in the way of it and stop its motion.
Imagine firefighters are spraying a building with steady streamline water from a firehose. The pressure that exists inside the stream of water (pushing outward against air pressure) as it flies toward the building is different from the pressure caused when the water strikes the building and changes momentum due to a collision.​

The pressure exerted by a fluid that strikes a barrier that stops its motion is different from the pressure internal to the fluid. The inverse relationship between pressure and speed only describes the pressure pushing out from the fluid itself, not the pressure exerted by the fluid being forced to a stop. The latter pressure is what the question describes, and it can much more accurately be described by the conversion of kinetic energy into work, which matches with intuition: the higher the kinetic energy, the greater the amount of work the fluid will do when it comes to a stop.

So the official answer to the question is wrong, the actual correct answer is A: releasing dam water faster will cause it to exert more force on the piston that releasing it slower.

 

[Nidum]

If the system is composed of a high level water tank connected by a pipe to a low level cylinder + piston and there is no movement of the piston or drain off of water anywhere then none of the given answers is correct .

Problem is that the question implies that changing water velocity is both possible and relevant to getting the answer .

In reality you just have a static hydraulic balance condition . The water is not moving at all .

 

[Mike Dacre]

Yeah, I thought of that, but the question says that the water is being released and that the operator controls the water speed. Would it not be the case that the speed that the water initially strikes the piston with would result in a greater total movement of the piston? Taking absurd examples, water striking a piston at 200 kmh would move the piston dramatically (or possibly destroy it) before coming to a stop. In contrast water released at 1 kmh would trickle up against to piston and only move it once sufficient weight was present.

I suppose that if the piston could move both ways, and it was not destroyed by the initial water flow, then when the water stops moving in either case the piston would end up in the same place, it is just that it would have a greater initial motion in the fast water case.