Calculate Water Flow in 10mm Pipe w/ 5 Bar Pressure

In summary, The conversation is about pipe flow analysis and how to take pressure into consideration. The use of the Darcy-Weisbach formula and the Bernoulli equation is discussed, as well as the Colebrook formula for implicit equations. It is recommended to use explicit equations for friction factor and to equate all fluid restrictions into a single factor known as the "resistance coefficient" (K). This factor can be plugged into the Darcy-Weisbach equation to take pressure into consideration.
  • #1
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I have a length of pipe 10 mm inside diameter, and a pressure of 5 bar. At the end I require about 0.2 l/s.

I know of the equation area=flow/velocity, A=q/c, but this doesn't take the pressure into consideration. How can I do this?
 
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  • #2
Hi TSN. I've attached a couple of examples of pipe flow analysis out of my college textbook. The first one, 7.3, shows the use of the Darcy-Weisbach formula for a horizontal pipe. The second one, 7.4, shows a pipe with a change in elevation such that the "energy equation" (ie: Bernoulli equation) must also be used. Example 7.4 also describes the use of the "Colebrook formula". Note that the Colebrook formula is only an implicit equation which relates friction factor, Re, surface roughness and pipe diameter, so you still need to use the Darcy-Weisbach equation. Alternatively, (and I would strongly recommend) you can use the Darcy-Weisbach equation directly by using explicit equations for friction factor such as those found here:
http://www.eng-tips.com/faqs.cfm?fid=1236

See also post #10 here:
https://www.physicsforums.com/showthread.php?t=152479

Note that for various fluid restrictions such as entrance and exit losses, pipe contractions or expansions, elbows, valves and other restrictions, you should get to know how to equate all of those restrictions into a single factor known as the "resistance coefficient" (K). That factor, K, is well defined by the Crane paper #410.

K = f L / D

which can be plugged directly into the Darcy-Weisbach equation.
 

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  • Pipe Flow Examples.pdf
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  • #3
the velocity is taking care of pressure here... flow=area*velocity

Bernoulli relates the velocity with the pressure...
 

1. What is the formula for calculating water flow in a 10mm pipe with 5 bar pressure?

The formula for calculating water flow in a pipe is Q = A*V, where Q is the volumetric flow rate, A is the cross-sectional area of the pipe, and V is the velocity of the water. In this case, the cross-sectional area of the 10mm pipe can be calculated using the formula A = π*r^2, where r is the radius of the pipe. Once the cross-sectional area is known, the velocity of the water can be determined using the Bernoulli's equation.

2. How do I calculate the cross-sectional area of a 10mm pipe?

The cross-sectional area of a pipe can be calculated using the formula A = π*r^2, where r is the radius of the pipe. In this case, the radius would be 5mm (half of the diameter), so the cross-sectional area would be approximately 78.5 mm^2.

3. What is the Bernoulli's equation and how is it used to calculate water flow?

Bernoulli's equation states that the total energy of a fluid in a pipe is constant at any point along the pipe. This equation takes into account the pressure, velocity, and height of the fluid. In order to calculate water flow, the velocity of the water can be determined using Bernoulli's equation and then plugged into the formula Q = A*V.

4. Can I use the same formula to calculate water flow in different pipe sizes and pressures?

Yes, the same formula Q = A*V can be used to calculate water flow in different pipe sizes and pressures. The only difference would be in determining the cross-sectional area and the velocity of the water using Bernoulli's equation.

5. How accurate is the calculated water flow in a 10mm pipe with 5 bar pressure?

The accuracy of the calculated water flow will depend on the accuracy of the inputs used in the calculations. If the cross-sectional area and velocity of the water are determined accurately, then the calculated water flow should also be accurate. However, there may be other factors that can affect the actual water flow, such as friction and turbulence in the pipe. It is important to consider all factors and use the most accurate inputs possible for the most accurate calculation.

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