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 )

 

[PJC01]

Dear reader,

Bernoulli's principle is a fundamental concept in fluid dynamics that explains the relationship between flow rate, velocity, and pressure in a fluid. It states that as the speed of a fluid increases, the pressure decreases and vice versa. This principle is essential in understanding how fluids move through different systems, such as pipes and tubes.

In the example of a shower, you are correct in saying that increasing the pipe diameter will increase the pressure and decrease the velocity, resulting in a more forceful shower. However, this is not always the case in all practical applications. In the case of filling up a bathtub, the main factor that affects the filling time is the flow rate, not the pressure. Therefore, the most efficient way to fill a bathtub would be to increase the flow rate by using a larger diameter pipe.

To understand this, let's look at the equation for flow rate: Q = A x V, where Q is the flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the fluid. As you can see, the flow rate is directly proportional to the pipe's cross-sectional area, meaning that a larger pipe diameter will result in a higher flow rate.

In summary, while Bernoulli's principle is essential in understanding the relationship between velocity, pressure, and flow rate, it is not the only factor to consider in practical applications. In the case of filling a bathtub, increasing the pipe diameter will result in a higher flow rate and a faster filling time. I hope this helps clarify any confusion you may have had.