if we have a pipe system like in the figure below where a pump exist in the system in order to deliver 200 gpm of water from the tank "A". we need to deliver 150 gpm from "C" and 50 gpm from "D" usually we use the pipe flow chart of william hazen in order to size each pipe according to its flow from the chart we get the head loss per 100 feet of each pipe and finaly we calculate the head of the pump according to the path that have the bigger head loss. my question is : in the problem below if we apply bernoulli equation between point "A,the top of the tank " and point "C" and between point "A" and point "D" and ignoring the dynamic energy effet cause it is small we get the head loss between these 2 paths are equal , but if we use william hazen equation and putting for each path a flow rate we get different head losses ,is there a contradiction ?? A-C bernoulli equation : 0 pressure + 0 velocity =HEAD LOSS THROUGH THE PATH -hEAD OF PUMP +Height between the top of the tank and point C so the head loss through the path ABC is equal to head of pump + heaight between top of the tank and point C now : A-D bernoulli equation we will get the same Head loss . but using william hazen equation each path has different head loss. is there a contradiction or not ?
firavia how r u ?? well in this case you will make normal calculations till you reach the point of the branched system T and then you will study for single pipe each time and you will get the head losses but u must know both head losses are the same because your pump dischargin to atmospheric pressure
Thank you for your answer , what if I have 2 other branches , the operation get more complicated if I want to apply bernoulli equation for each branch + the common line , but if I use hazen william flow chart to estimate the diameter of each branch according to the flow rate of each one it is not going to be accurate at all , cause how can I estimate a diameter by assuming a flow rate and a slope <ft/100 ft head loss slope > , usually this chart to determine the head loss in a pipe when we have the diameter of each pipe and the flow rate , but in the case of pipe sizing I dont think it works cause we are assuming 2 values out of 3<flow rate and head loss in order to determin the diameter> am I right ? if yes is there any other method for pipe sizing ?.
Hi firavia, There's a good pipe flow analysis paper I posted on this thread: https://www.physicsforums.com/showthread.php?t=234887 Take a look at page 15. It shows how to do piping networks there, but you'll need to understand how to do a single pipe run first. Bernoulli's is only used to determine changes in pressure due to velocity and elevation as shown on page 14. Basically, head loss due to flow restrictions are permanent losses that are unrecoverable, unlike the other terms in the Bernoulli equation. See if you can work through some of this and get some understanding on how to use the Darcy-Weisbach equation first. You may also consider getting a copy of the Crane Technical Paper #410. It's cheap but it's become a standard in the industry which has been built upon by others for one dimensional flow losses.
can we establish bernoulli equation + darcy equation added to it to calculate the head loss in the pipes as the following , according to the picture: P"A"/Guamma +V"A"square / 2.g = hEAD loss throug the main pipe and the pipe"BC" + elevation from the top of the tank to point B +V"C"^2/2.g -Head of pump . is the equation established above is correct ana balanced , if yes then the head loss in pipe BC is very slightly different thn the head loss in Bd because od the difference in discharge velocity at both pipes am I correct ? cause if we take the path ABD we the equation is : P"A"/Guamma +V"A"square / 2.g =P"D"/guamma "which is zero-atmospheric" +V"D"^2/2.g+ead loss all alon the path ABD + HEAD OF PUMP +elevation from the top of the tank to B , the difference in head loss of this path and the path of ABC is the difference in dynamic energy at discharge of the 2 pipes BD and BC , am I correct ? pleas confirm.
The Hazen-Williams is an empirical formula and doesn't have a theoretical basis. It is only meant to be used for water flowing in a single pipe for a specific range of pipe diameters. It cannot be used to analyze a parallel pipe network. EDIT: I should probably clarify that H-W can be used for estimating the head loss instead of Darcy during a network analysis but you cannot just simply compare the head losses for two single pipes. The head loss in each branch will be the same since the fluid ends up at the same energy state at the outlet node (atmosphere in this case). CS