Bernoulli's principle, flow rate, velocity and pressure

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Discussion Overview

The discussion revolves around Bernoulli's principle and its implications for flow rate, velocity, and pressure in practical applications, particularly in the context of household plumbing scenarios like showers and bathtubs. Participants explore how pipe diameter affects these variables and seek clarity on maximizing water pressure and filling rates.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant notes that decreasing the diameter of a pipe leads to increased velocity and decreased pressure, but struggles to apply this to practical situations.
  • Another participant suggests that to maximize water pressure in a shower, one might consider increasing the pipe diameter for a given flow rate.
  • There is a question about the optimal pipe size for filling a bathtub quickly, with uncertainty about whether a larger diameter would be beneficial for speed or volume.
  • A later reply introduces the concept of dynamic pressure, explaining that it increases with fluid velocity, while static pressure decreases according to Bernoulli's equation.
  • It is mentioned that the pressure supplied to the water is independent of the pipe geometry used for delivery.
  • Another participant cautions that Bernoulli's equation should be applied with care, emphasizing the need for a closed system and inviscid flow conditions.

Areas of Agreement / Disagreement

Participants express varying interpretations of how pipe diameter affects flow rate and pressure, indicating that multiple competing views remain. The discussion does not reach a consensus on the best approach for maximizing flow in practical applications.

Contextual Notes

Limitations include assumptions about the flow being inviscid and the system being closed, which may not hold in all practical scenarios. The relationship between flow rate, pipe diameter, and pressure is complex and context-dependent.

sanzenbacher
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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.
 
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sanzenbacher said:
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.
 
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.
 
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 )
 

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