Fluid dynamics: pressure in pipes

[ikihi]

So I've been discussing this problem with my plumber dad. I uploaded the picture.
I'm wondering if the pressure would change in the red pipe since the diameter decreases to 4 cm. Assume the 1st 10 cm pipe is full with water.

Question: If the home pressure is 517 kPa going through first pipe, would the pressure and velocity of water increase locally in the red pipe?

 

[Andrew Mason]

So I've been discussing this problem with my plumber dad. I uploaded the picture.
I'm wondering if the pressure would change in the red pipe since the diameter decreases to 4 cm. Assume the 1st 10 cm pipe is full with water.

Question: If the home pressure is 517 kPa going through first pipe, would the pressure and velocity of water increase locally in the red pipe?

The flow rate has to be the same in all 3 sections. So the speed of the fluid has to increase in the red section and then decrease in the next black section. In speeding up the fluid gains kinetic energy.

Pressure represents energy density - potential energy per unit volume. Assuming there is minimal energy loss in the pipe, the energy in the fluid must be conserved. So any gain of kinetic energy must come from a drop in pressure.

So the pressure in the red pipe is lower. This is Bernoulli's principle.

AM

 

[ikihi]

The flow rate has to be the same in all 3 sections. So the speed of the fluid has to increase in the red section and then decrease in the next black section. In speeding up the fluid gains kinetic energy.

Pressure represents energy density - potential energy per unit volume. Assuming there is minimal energy loss in the pipe, the energy in the fluid must be conserved. So any gain of kinetic energy must come from a drop in pressure.

So the pressure in the red pipe is lower. This is Bernoulli's principle.

AM

I see. So in middle red pipe, the fluid will increase in velocity which causes less pressure on water in that pipe in the system. That's kind of funny. At first I thought there would be more pressure on the smaller pipe, but it makes sense now.

 

[Andrew Mason]

I see. So in middle red pipe, the fluid will increase in velocity which causes less pressure on water in that pipe in the system. That's kind of funny. At first I thought there would be more pressure on the smaller pipe, but it makes sense now.

That's right. We tend to think of fluid confined to a smaller space as having higher pressure. But this is does not involve the compression of fluid. The density of the fluid is the same throughout the pipe system.

You can think of it this way: a pressure difference between the larger pipe and the smaller pipe is needed to accelerate the water in the smaller pipe. So the pressure in the larger pipe has to be higher. On the other end, the fluid in the smaller red section must slow down when entering the larger section, so the pressure must again be higher in the black section than in the red.

AM