Richard, a 22 year old male from Halifax, N.S. asks on July 21, 2006,

How do you calculate water flow rate (volume/sec) based on water pressure and hole or pipe size? And is it the same based on water pressure created by gravity (water tower PSI) and pressure created by compression like a hole in the bottom of a boat which is 30ft underwater (underwater PSI)?viewed 14965 times

To answer the second question first, yes, there is only one kind of pressure. `Underwater PSI' and `Water tower PSI' are both created by gravity. We can calculate the flow rate using Newton's second law:

force = mass * acceleration,

Suppose we have a hole of area A, and the pressure differential across the hole is p. Then a force Ap acts on the water at the hole.

Suppose the water flows through the hole at a rate u m/s. Then in one second, a mass uAd flows through the hole, where d is the density of water in kg/m^3. This mass has been accelerated from rest to a velocity u in one second, so it has undergone an acceleration u m/s^2. So from Newton's second law,

Ap = u^2 A d

So u = square_root_of(p/d), And if you want the fluid flow rate as a volume/sec, it's

Q = A * square_root_of(p/d)

This analysis leaves some things out -- for example, it takes no account of the shape of the hole, or how thick the wall surrounding the hole is. These things are usually included in a numerical `K' factor, a number close to unity which can be looked up.

If instead of a short hole you've got a long pipe, you would need to calculate the pipe friction and subtract the frictional force from the force due to pressure. The friction produces an effective reduction in the pressure of

Delta p = dfLu^2/2D

where L is the pipe length, D its diameter, and f the friction factor, which depends on the flow rate and the roughness of the pipe's inner surface in a rather complicated way, usually summarised by a Moody diagram.

Note: All submissions are moderated prior to posting.

If you found this answer useful, please consider making a small donation to science.ca.

- Canadian Nuclear Safety Commission Educational Resources
- National Inventors Hall of Fame
- JUMP Math
- Society for Canadian Women in Science and Technology
- SciQuest e-Solutions for Science
- Natural Sciences and Engineering Research Council of Canada
- Manning Awards for Innovation
- Royal Society of Canada
- Geological Survey of Canada
- Canadian Networks of Centres of Excellence
- Canadian Landscapes at Natural Resources Canada
- Canadian Association of Physicists
- A Century of Innovation
- Understanding Science
- AlphaGalileo
- National Film Board of Canada Youth Science
- PICS Climate Insights 101
- Canadian Association for Girls in Science
- Virtual Library for the History of Science
- The Chemical Institute of Canada
- Canadian Biotechnologist 2.0
- ISI Highly Cited Scientists
- Deep River Science Academy
- Journal of the History of Canadian Science
- Wikipedia
- Innovation Canada
- Mars Society
- Nobel Prize Archive
- science.gc.ca
- Online Science & Engineering Encyclopedia
- CurioCity
- Canadian Nuclear FAQ
- Association of Science Communicators
- Astrofiles
- Wilderness Astronomy