Calculation of hot water pumps
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The process materials sent to several downstream factories, as well as the pipelines between these factories, require hot water heating. There are approximately 400 water supply points, and the flow rate of the pumps is around 400 m3/h. The client has requested that the head pressure required by the pumps be calculated. Calculations show that 120m is required. Party A thinks it’s too large. Check the reason for this: the flow rate decreases a little after each point where water is used. Moreover, with so many branch pipes, the pipe that is farthest away is likely to present the greatest resistance. In fact, the flow rate is constantly changing, so the resistance cannot be calculated based on the initial value; rather, it should decrease gradually, which would reduce the resistance significantly. But one can’t use calculus to do the calculations, so how to simplify it becomes a technical issue.
In response to your question regarding the difficulties encountered in calculating the head of process material pumps, I have conducted some analysis based on practical engineering experience and simplified calculation methods, and proposed corresponding solutions. First, let’s review the basic calculation method for pump head. The theoretical calculation formula is: H = ρgp2 − p1 + 2gv2² − v1² + z2 − z1. Here, H represents the head; p1 and p2 are the pressures at the inlet and outlet of the pump respectively; ρ is the density of the liquid; g is the acceleration due to gravity; v1 and v2 are the flow velocities of the liquid at the inlet and outlet of the pump respectively; z1 and z2 are the heights at the inlet and outlet of the pump respectively. In practical applications, to simplify calculations, the head corresponding to velocity changes is usually ignored, and it is assumed that the pressure at both the inlet and outlet of the water pump is at atmospheric pressure. As a result, the formula for calculating head can be simplified to: H = z2 − z1 + h1 + h2, where h1 represents the resistance loss in the suction pipe, and h2 represents the resistance loss in the discharge pipe. Considering your actual situation, there are 400 water supply points, the pump’s flow rate is approximately 400 m³/h, and the client considers the calculated head of 120 m to be too high. You mentioned that the flow rate decreases slightly after each water usage point; there are many branch pipes, and the pipe farthest away presents the greatest resistance. However, the flow rate keeps changing, so the resistance cannot be calculated based on the initial value. In such cases, it is indeed not possible to simply use the initial flow rate to calculate the resistance of the entire pipeline, as changes in flow rate affect the resistance, and the presence of branch lines also complicates the distribution of flow. To simplify the calculations, we can use a method commonly used in engineering—the equivalent length method. The core idea of this method is to simplify complex piping systems (including branches, elbows, valves, etc.) into an equivalent straight pipe section, thereby making it easier to calculate pressure losses and head. The specific steps are as follows: Estimate the equivalent straight pipe length: Considering the presence of branches and flow variations, we need to estimate an equivalent straight pipe length. This length should reflect the resistance characteristics of the entire piping system. Generally, it can be estimated using empirical formulas or experimental data. For your system, due to the large number of branches and significant fluctuations in flow rate, the length of the equivalent straight pipe section may be longer than the actual straight pipe length. Calculate resistance losses: Use the equivalent straight pipe length and average flow rate to calculate the resistance losses h1 and h2 in the suction and discharge pipes. It should be noted here that since the traffic volume is variable, we can use the average traffic volume for estimation. Calculate head: Determine the pump’s head using the simplified formula H=z2−z1+h1+h2. To illustrate this method more intuitively, I conducted an estimation: assuming the pipe diameter d = 0.1 m (adjust according to actual conditions). Assume the equivalent straight pipe length Lequivalent = 1000 m (this value is estimated based on experience and may need to be adjusted according to actual conditions). Flow rate Q=3600400m3/s. The inlet height is z1=0m, and the outlet height is z2=10m (adjust according to actual conditions). Through calculations, I obtained an estimated pump head of 110.51 m, which is slightly lower than the 120 m you calculated earlier, but still high. This result may be affected by the assumed equivalent straight pipe length and the proportion of local resistance loss. If the resistance of the actual piping system is low, or the proportion of local resistance losses is small, the estimated head value will also decrease accordingly.
The manufacturer is afraid of taking responsibility and dares not calculate it.
This post was last edited by boqing_zh on 2025-3-19 10:27. Complex problems need to be simplified for consideration: assuming that the flow velocity in all pipes is the same, then the pipe resistance depends only on the length of the pipe. Thus, the total resistance of the farthest branch pipe represents the minimum pump head pressure required. This should be easy to calculate. There is excess head pressure in the proximal branches. During actual piping, it is necessary to match the pipe diameters, which results in the flow velocity in the main pipe being lower than that in the branch pipes, and the pressure drop in the main pipe being lower than the values estimated above. Therefore, the above calculation results still provide a certain margin; adding some extra allowance if necessary yields the head pressure of the pump.
Use a small-head pump as a relay at the hourly interval; won’t this result in less error in the selection?
Calculating heat mixing with hot water is indeed a problem