Hi every one here.
Torricelli's theorem says that the velocity of fluid flowing out of an opening relates to the height of fluid above the fluid. Ok. Now in the file (Torricellis theory.rar) attached I tried to simulate and model this theory with watergems V8.
I set below specifications for reservoir, pipe and junction at model:
R-1: Elevation= 10 m
P-1: Length= 10m
Diameter= 1000 mm
Hazen-williams C= 999.999
J-1: Elevation= 0 m
Demand=100.000 l/s.
As you see, the specifications for pipe somehow designed to minimize the headloss (almost zero).
Now, according to torricelli's theorem, the velocity of water in pipe must be 14 meter per second [V=(2*g*10)^.5=14]. But if you set 100.000 liter per second for J-1 as demand, and run the model, then the velocity of water in P-1 will be over 127 meter per second. How this incoherence should be explained?
By the way, if you send your response to my Gmail directly, it will be appreciated much.
Thanx a lot.
Mohsen.amiri@gmail.com
Mohsen,
Torricalli's theorem assumes free discharge to the atmosphere but the way you have set up the model is to force a known flow through the pipe. That flow serves as the basis for the velocity calculation using V = Q/A.
If you want to model free discharge to the atmosphere, consider using an emitter coefficient at the junction or model the flow using pressure dependent demand and set up the PDD function to correspond to Torricelli's theorem.
Tom
Hi Tom
Thank you.
would you please explain more how I can model the law? I mean PDD function & emitter coefficient you wrote.
My first question would be "why are you using a network model to solve this?'. What is the practical use case? You can solve this on a picket calculator.
I do not want to solve anything with it. It is just because of my curiosity :)
Now explain please.
The emitter coefficient is defined as the K in
Q=Ksqrt(P)
and Torricelli equation solved fro flow is
Q = A sqrt(2gh)
Assuming h and P are in same units
K = A sqrt(2g)