Chapter 5 – Surge Protection
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Surge Analysis and the Wave Plan Method
Supplementary Material: Example Problems and Solutions
Chapter 5 – Problem 5.2
5.2 For the pressure relief valve described in the previous example, what is the longest possible time required to fill the diaphragm chamber avoiding drip flow across the tapping points A and C? What should the minor loss coefficient of the needle valve be to limit the flowrate to the desired value? What is the associated resistance across the needle valve? What is the ratio of the open area of the needle valve when it is closed to the point of drip flow with respect to the fully open area of the valve?
In household faucets, a drip flow of roughly 4000 drops amount to 1 liter of water with an approximate drip size of ¼ ml (https://water.usgs.gov/edu/activity-drip.html). The fastest possible drip flow is about 240 drips per minute (after that the flow is usually considered to be continuous).
240 drips per minute = 60 ml/min or 1 ml/s or 0.001 l/s or 0.000001 m 3 /s.
Therefore, the longest possible time required to fill the 1-liter volume of the diaphragm chamber (avoiding drip flow) is 1000 s.
Velocity associated with 0.000001 m 3 /s flowrate = 0.0796 m/s
50.98 = (0.0796 2 ) * [ (0.015 * 1 /(2 * 9.81 * 0.004)) + (m / (2 * 9.81))]
m ’ = 8050.248 * (2 * 9.81) = 1641.23
Resistance = K = headloss across the needle valve / Q 2 = ∆H n / Q 2
K = (m v 2 /(2g)) / Q 2 = 1641.23 * 0.0796 2 / (2 * 9.81 * 0.000001 2 ) = 0.5297E+12
The area ratio for any valve is related to its resistance ratio by an inverse square root relationship as described in Section 4.1 of the book “Pressure Wave Analysis of Transient Flow in Pipe Distribution Systems” by Wood, Lingireddy and Boulos (2005).
A o /A f = √(K f /K o ), where K f is the resistance of a fully open valve with an area of A f and K o is the resistance of a partially closed valve of area A o .
K f = (mv 2 /(2g)) / Q 2 = 3* 12.17 2 / (2 * 9.81 * 0.000153 2 ) = 9.67E+08
A o /A f = (9.67E+08 / 0.5297E+12) 0.5 = 0.0427 A o is roughly 4% of full open area.
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