TECHNICAL
Image 1: The four key factors needed when calculating NPSHa (Image courtesy of Jim Elsey and Summit Pump, Inc.).
The three remaining terms (V, S, F) are all negative and their sum total will be subtracted from the A term (ten metres), we can also reason that the sum of the three remaining terms must be ≤ 5.5 metres or the pump will not work properly. Assume the absolute total of the three terms is X and solve for X. Equation 4 (10- X = 4.5) solve for X yields 10 – 4.5 = 5.5 From this step, you can surmise that the total (absolute) values of V, S and F must be less than 5.5 metres.
Lift or (Negative) Static Head (S)
For the next step in the example, we will establish the negative static head (the lift) as 2.5 metres. Note that this term is an actual measurement, not a calculation. Consequently, the S term in our simplified Equation 5 now has a value of 2.5 metres. If S is 2.5 metres, then the sum of friction F and vapor pressure V total must be less than three metres. Equation 5 5.5 = V + S + F S was measured at 2.5 metres, so: 5.5 = V + 2.5 + F therefore: 3 = V + F We need to view this as 3 ≥ V + F, where we are expressing the terms in their absolute values and not the negative terms from the formula. You can look at this mathematically, but I think it is more important to look at it as you have limits on how much friction and vapor pressure can be present. If the value is exceeded, the pump will not operate properly or at all.
Friction Factor (F)
Before we address the vapor pressure, I want to skip ahead to the friction factor F. The total friction head was calculated at 1.11 metres, but to be conservative and to also allow for “aging” of the system, we will round off to 1.2 metres of friction head. Now we have a value of 1.2 metres to assign to the F term in the equation. From this, we can calculate that we now have 1.8 metres of possible margin before we calculate the value of the vapor pressure term (Equation 6). Equation 6 3 = V + 1.2, or V = 1.8, and again we should think of this as V ≤ 1.8
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pump industry | Summer 2022 | Issue 38
Vapour Pressure (V)
Vapor pressure in the US-C system is normally expressed in pounds per square inch absolute (psia), consequently you will need to convert to head ([psi X 2.31] ÷ [specific gravity] = head of vapor pressure absolute). In the SI system, vapor pressure may be expressed in pascals or kilopascals (kPa) or even sometimes in Torr or mmHg. Regardless, you will need to convert to metres of head (absolute) to work the factor in this equation. The V term (vapor pressure) seems to be an almost insignificant factor for liquid temperatures near ambient, which can be misleading and lure you into the false sense that it is not important. For a more detailed explanation of vapor pressure, please refer to my detailed column in the April 2018 issue of Pumps and Systems magazine. Realise that as the liquid temperature increases, so does the vapor pressure (V) and it does so at an exponential rate. At around 20°C (68°F), the value of V would only be 0.237 metres (0.78 feet) absolute, but at 32.2°C (90°F) it would increase to 0.494 metres (1.62 feet) absolute and at 71°C (160°F), it would be 3.42 metres (11.21 feet) absolute, and at 93.3°C (200°F) it would be 8.43 metres (27.65 feet) absolute. Hint: this is the main reason you will not see a self-primer on applications with a static lift at liquid temperatures over 62°C. You do not need to calculate the value of vapor pressure, you simply look it up in a handy-dandy trusted chart. I like to use the Cameron Hydraulic Data book. For our example, let’s assume the water is 25°C and so the corresponding V will be 0.3232 metres absolute, which I will round off to 0.32 metres absolute. With this value of 0.32 metres for the vapor pressure, we can finalise/satisfy our equation (Equation 7). Equation 7 V ≤ 1.8? Yes, 0.32 is less than 1.8 We can surmise that this application will work, and we even have an extra margin of approximately 1.5 metres.
Priming Time – Don’t Wait Too Long
In the previous example, the water was near ambient temperature and the pump was close to the sump (suction source) with a properly sized suction pipe. I recently witnessed performance issues with two separate installations where the pumps were placed a long distance from the sump, and in one instance the suction pipe was several sizes bigger than it needed to be.
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