Simplifed Water Hammer Calculation
Simplifed Water Hammer Calculation
(OP)
Just one more thought on the water hammer thread - it's true that the correct and standard method is a highly professional task, separating harmonic DE's as per the method of characteristics, but there is an easy approximation that does just as well:
For a slow control operation such as closing a valve, the time of closure tc has to be greater than the return time tr = 2L/c where L is the length of pipe and c is the celerity. This ensures that the positive pressure wave is reduced by the returning negative wave.
You can use this to design a closure time tc > tr that reduces the positive pressure surge to whatever your design safety pressure is, say Pdesign = 100 kPa.
The idea is to assume a constant flow deceleration from your start flow velocity V1 down to zero, in the interval of your closure time tc - this is not too far from reality and you can experiment with closure rates to get it close to a constant rate of pressure increase, which is the effect you need.
The deceleration is then approximately dV/dt = V1/tc (tc still unknown) and constant. The rate of pressure increase is then constant as per compression-continuity, ie
dP/dt = (density x c) x dV/dt = (density x c) x V1/tc
(This is from DP = (d x c) x V1 - just differentiate wrt time)
OK, so you have a pressure increase rate. The pressure will increase up to the moment when the return wave arrives, after which it is effectively reduced by the negative pressure going in the other direction. The maximum pressure occurs at the return time, tr = 2L/c, and has a value of
Pmax = dP/dt x tr
= (d x c x V1 / tc) x (2L/c)
= 2d x V1 x L/tc
Which is nicely free of the large celerity c. Assuming a design pressure Pdesign that your system can't exceed, and a safety factor (say 2 to be really safe), you get
Pmax = 2 x Pdesign = 2d x V1 x L/tc
Which allows you to solve for the closure time tc:
tc = d x V1 x L / Pdesign
eg for Pdesign = 100 kPa, V1 = 2 m/s, L = 1000 m -> tc = 20 seconds
- I think this what Jeffvalve had in mind when he was trying to recall the method - I think I'm just reminding him.
Regards, Mike Eleven
thread408-81043: Water Hammer Formula
For a slow control operation such as closing a valve, the time of closure tc has to be greater than the return time tr = 2L/c where L is the length of pipe and c is the celerity. This ensures that the positive pressure wave is reduced by the returning negative wave.
You can use this to design a closure time tc > tr that reduces the positive pressure surge to whatever your design safety pressure is, say Pdesign = 100 kPa.
The idea is to assume a constant flow deceleration from your start flow velocity V1 down to zero, in the interval of your closure time tc - this is not too far from reality and you can experiment with closure rates to get it close to a constant rate of pressure increase, which is the effect you need.
The deceleration is then approximately dV/dt = V1/tc (tc still unknown) and constant. The rate of pressure increase is then constant as per compression-continuity, ie
dP/dt = (density x c) x dV/dt = (density x c) x V1/tc
(This is from DP = (d x c) x V1 - just differentiate wrt time)
OK, so you have a pressure increase rate. The pressure will increase up to the moment when the return wave arrives, after which it is effectively reduced by the negative pressure going in the other direction. The maximum pressure occurs at the return time, tr = 2L/c, and has a value of
Pmax = dP/dt x tr
= (d x c x V1 / tc) x (2L/c)
= 2d x V1 x L/tc
Which is nicely free of the large celerity c. Assuming a design pressure Pdesign that your system can't exceed, and a safety factor (say 2 to be really safe), you get
Pmax = 2 x Pdesign = 2d x V1 x L/tc
Which allows you to solve for the closure time tc:
tc = d x V1 x L / Pdesign
eg for Pdesign = 100 kPa, V1 = 2 m/s, L = 1000 m -> tc = 20 seconds
- I think this what Jeffvalve had in mind when he was trying to recall the method - I think I'm just reminding him.
Regards, Mike Eleven
thread408-81043: Water Hammer Formula





RE: Simplifed Water Hammer Calculation
NO IT DOESNT! It doesnt account for instances where they may be column separation.
Valve closure may be linear but the affects on pressure are far from that. How does your formula account for the characteristics of the valve.
RE: Simplifed Water Hammer Calculation
RE: Simplifed Water Hammer Calculation
Don't know anything about water hammer calculations but basically what you're saying is that if:
Pipe lenght: l
Density: d
Flow velocity: w
Closing time: t
Mean pressure: p
(Pipe area: A)
(Pipe volume: V)
The mass of the water in the pipe is m= V*d = A*l*d
and you accelerate that mass from the velocity w to 0 in t
F = m*a = A*l*d*(w/t)
The force is acted by the blockage with an area of A so
p = F/A = A*l*d*(w/t)/A = (l*d*w)/t
And as the returning wave adds with the acted pressure
p,max = 2*p = 2*(l*d*w)/t
If the operating pressure is p0 then i could assume
p,design = p0 + p,max = p0 + 2*(l*d*w)/t
Don't know if it's correct, but it sounds good. In the end of your excellent post i assume you by mistake divided with the safety factor instead of multiplied.
regards
Drex
RE: Simplifed Water Hammer Calculation
Also yes that's correct the method does not account for valve characteristics - you need to experiment with valve closure rates to ensure a constant pressure increase rate, or modify the formula with the actual rate. It's a simple approximation as I said, I'm glad that I rang your alartm bells.
The idea of the formula is to find a conservative (safe) slow closure time to avoid major positive and negative pressure shocks - so that column separation in particular does not occur. I guess I'm frustrated that the standard solutions are outside even a mid-career practitioner's reach, and so they may rely on even simpler approximations such as tc = 20 x the return time, which is only right if that's in your working pressure range, but in softer systems - BOOM!
So the formula is a rational method, which with CORRECTLY APPLIED SAFETY FACTOR (my bad!) should keep you out of trouble.
Regards, Mike Eleven
RE: Simplifed Water Hammer Calculation
RE: Simplifed Water Hammer Calculation
The cost of software is far less than you imagine. he time to understand the dynamics in a system is far more. But you need to understand that to do it by manual calculation.
Download the AFTImpulse software demo and play around. Once you can use this software for your steady state and transient analysis it will be used frequently. www.aft.com
RE: Simplifed Water Hammer Calculation
RE: Simplifed Water Hammer Calculation
Mike