Enter the fluid density, wave speed (or compute it), pipe length, valve closure time, and the initial/final velocity (or flow rate and pipe diameter) into the calculator to determine the surge pressure rise and the resulting maximum pressure.
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Surge Pressure Formula
The following formulas are commonly used to estimate the surge (water hammer) pressure rise from a valve closure.
\Delta P=
\begin{cases}
\rho\,a\,\Delta V, & t_c \le \frac{2L}{a}\\
\frac{2\rho\,L\,\Delta V}{t_c}, & t_c > \frac{2L}{a}
\end{cases}- Where ΔP is the surge pressure rise (Pa, psi, etc.)
- ρ is the fluid mass density (kg/m³)
- a is the pressure wave speed (m/s)
- ΔV is the change in flow velocity (m/s)
- L is the pipe length (m)
- tc is the valve closure time (s)
To estimate surge pressure rise, determine the wave travel time (2L/a). If the closure time is less than or equal to 2L/a (rapid closure), use the Joukowsky equation ΔP = ρaΔV. If the closure is slower than 2L/a, a common approximation reduces the peak rise roughly in proportion to (2L/a)/tc.
How to Calculate Surge Pressure?
The following example problem outlines how to calculate the Surge Pressure rise.
Example Problem #1:
- First, determine the fluid density. In this example, the density is 1000 kg/m³ (water).
- Next, determine the wave speed. For this example, assume a = 1200 m/s.
- Determine the pipe length and closure time. Let L = 300 m and tc = 0.2 s, so 2L/a = 2(300)/1200 = 0.5 s. Since tc ≤ 2L/a, treat this as rapid closure.
- Determine the change in velocity. If the flow drops from v1 = 1.5 m/s to v2 = 0 m/s, then ΔV = 1.5 m/s.
- Finally, calculate the surge pressure rise using ΔP = ρaΔV.
ΔP = ρ * a * ΔV
Inserting the values from above and solving the equation:
ΔP = 1000 * 1200 * 1.5 = 1,800,000 Pa = 1.80 MPa ≈ 261 psi
FAQ
What is Surge Pressure?
Surge Pressure, often referred to as water hammer, is a pressure change that occurs in a piping system when there is a sudden change in the flow velocity of the fluid within the pipes. This can happen due to the rapid closing or opening of valves, or the sudden start or stop of a pump.
Why is it important to calculate Surge Pressure?
Calculating Surge Pressure is crucial for the design and operation of piping systems to ensure their safety and reliability. High Surge Pressures can cause damage to pipes, valves, and other components, potentially leading to system failure, leaks, or even hazardous accidents.
Can Surge Pressure be mitigated or controlled?
Yes, Surge Pressure can be mitigated or controlled through various methods. These include the installation of surge tanks, air chambers, or valves specifically designed to relieve pressure. Additionally, gradual changes in flow velocity and careful operational practices can help reduce the risk of surge pressure spikes.
