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# gravity pipe flow calculator

Question:For laminar flow through a circular pipe of radius R, the velocity distribution takes the following form, v=(B/ )*[R^2 - r^2] Where B is a constant and is the fluid viscosity. What is the maximum velocity in terms of B, and R and the mass flow rate in terms of , B, and R? Im sorry, I still dont understand the part about how to obtain the mass flow rate. Could you elaborate? Do I have to integrate the equation do make a substitution?

Answers:1. Max velocity is = v = (B/ ).R and 2. Total flow F is calculated as the flow (velocity x area) in a concentric ring-shaped element of radial depth dr and therefore of area 2 .r.dr, integrated over r = 0 to R, giving: F = 2 (B/ ). . [R -r ].r.dr = 2 (B/ ). .[R r /2 r^4/4] from r=0 to r=R = (B/ ). [R^4 (R^4)/2] = (B/ ). .R^4 Note: strictly speaking to solve 1 we should have differentiated v wrt r and set the result = 0 to find the maximum. However in this case of a function as simple as (R -r ) it s easy to do it just by inspection.

Question:I have a pipe that is 1/2" in diameter and there is 50 psi running through it. If it were to be sheared off, I want to know what the volume flow rate of the water coming out of the pipe. Do do this I need to know the velocity of the water and I can't seem to figure out how to find it. Any help would be greatly appreciated.

Answers:If it is for a residential use, then 50 psi is a very normal pressure. There is no direct correlation between pressure and flow rate (a pipe not flowing can still have pressure), but a typical velocity for a 1/2" pipe should be less than 5 feet per second to keep water hammer from hurting plumbing fixtures. So, 5 fps translates to a little more than 3 gallons per minute. 3.06 to be exact.

Question:I need to calculate how much water will flow through 2 different size water lines, 1" and 1 1/2" diameter. The water lines are coming directly off 8" water main, using Type K Copper Tube. Estimated water pressure is 65 psi. The actual calculations will be greatly appreciated. There is a 1 1/2" pipe from the service main running 30 feet to the point that I am connecting to. There is no change in elevation. The only fitting is the meter which is the focus of my question/problem. The contract engineer wants to install a 1" meter (instead of the 1 1/2" meter that I believe should be used). I need to determine how much water will flow through each size meter (assume for the point of calculation that there is no "resistance", just the reduction in pipe size.) I have not been able to figure out how to use the bernouli equation. Beyond the meter point, there will be over 200 feet of pipe servicing multiple apartments.

Answers:http://en.wikipedia.org/wiki/Hazen-Williams_equation Is there any elevation change of 1" & 1-1/2" diameter pipes which must be taken into account? What is the estimated length of each of these lines? Edit: ( IMO, that's a long service line to those apartments. 1" and 1-1/2" diameter line may be insufficient depending on the number of apartment (fixtures) that are served. http://www.engineeringtoolbox.com/hazen-williams-water-d_797.html Sadly, I lack enough detail to give you any conclusive answer. The 2001 ASHRAE Handbook chapter 35 section 3 covers water piping design and R.B. Hunter's demand diversity estimation for residential buildings in good detail). Disc water meters are quite common. The Badger disc meters have a 3.4 and 4.8 PSI pressure loss at maximum design flow for the 1" and 1-1/2" meters respectively. 40 GPM @ 1" dia. http://www.badgermeter.com/getdoc/98f4a26e-5b06-495e-8a66-65cf55e7ed45/rd-t-55-pdf.aspx 80 GPM at 1-1/2" dia. http://www.badgermeter.com/getdoc/7fd0255f-bfef-47f8-a383-6538b93a7623/RD-T-1-1_2.aspx See pgs. 40-43 for an example of the engineering work that is involved http://www.quickscribe.bc.ca/images2/bcappp_2.pdf

Question:1. Describe and define the parameter involved in characterizing flow in pipe 2. Calculate the diameter of pipe to attain laminar flow for a fluid with kinematic viscosity of 1.12 x 10-6m2/s at 0.5m/s.

Answers:1] Reynolds number, D V density/viscosity 2] Laminar flow has Re <1000