Bernoulli's principle, flow rate, velocity and pressure

[sanzenbacher]

Hello,

I need some help understanding Bernoulli's principle, flow rate, velocity and pressure.

I understand that when the diameter of a pipe decreases, the velocity will increase and the pressure will decrease. But I am having a hard time applying this to a practical application.

For example, for a shower I would want to maximize the water pressure. So for a given flow rate I would want to increase the pipe diameter to increase the pressure.

But what about filling up a bath tub? For a given flow rate, what size pipe would fill up the bathtub the fastest? Would I want the opposite to increase the speed? Or do I still want a larger diameter so I have a greater volume of water?

I feel like I am not understanding something very basic here.

 

[Chestermiller]

Hello,

I need some help understanding Bernoulli's principle, flow rate, velocity and pressure.

I understand that when the diameter of a pipe decreases, the velocity will increase and the pressure will decrease. But I am having a hard time applying this to a practical application.

For example, for a shower I would want to maximize the water pressure. So for a given flow rate I would want to increase the pipe diameter to increase the pressure.

But what about filling up a bath tub? For a given flow rate, what size pipe would fill up the bathtub the fastest? Would I want the opposite to increase the speed? Or do I still want a larger diameter so I have a greater volume of water?

I feel like I am not understanding something very basic here.

Since filling the bathtub is based on volume of water in the tub, you want to maximize the volumetric flow rate.

 

[siddharth5129]

The quantity you're looking for is the DYNAMIC pressure of the fluid. This increases with increasing velocity of the fluid. Bernoulli's equation talks about the STATIC pressure at a point decreasing with increasing velocity for irrotational and inviscid flows. This is what a barometer attached to that point would measure. But the pressure at which your water is supplied is a third quantity and cannot possibly depend on what you choose to do with the geometry of the delivery pipe.

As for your second question, if you have a given flow rate (say 1 litre/min ) then a bathtub that has a 15 litre capacity will take 15mins to fill up. It doesn't matter what you do with the flow conditions at the outlet.

 

[siddharth5129]

A word of caution when you apply bernoulli's equation. It's simply a statement of energy conservation applied to fluid dynamics. So ensure your system is closed ( no energy or mass flow in or out ) and that the flow is sufficiently approximated as inviscid (no thermal losses )