HOW TO CALCULATE PRESSURE ANYWHERE IN A PUMP SYSTEM? Jacques Chaurette p. eng. April 2003

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1 HOW TO CALCULATE PRESSURE ANYWHERE IN A PUMP SYSTEM? Jaques Chaurette p. en. April 003 Synopsis Calulatin the total head of the pump is not the only task of the pump system desiner. Often we need to know the pressure level at a speifi point in the system. Suppose we have a system that transports a hot liquid, we know that hot liquids vaporize very easily under onditions of low pressure. There is a hih point in our system where we know the pressure will be low but exatly how low? The tehniques in this artile will show you how to do this alulation for any point in the system. Calulatin the pump total head sometimes involves alulatin the pressure in different parts of the system. For example, you may need to ensure that a iven piee of equipment has a ertain pressure level at its inlet to ensure proper operation. The manufaturer of the equipment will ive this pressure level if it is ritial. Or you may need to alulate the pressure level at the inlet of the ontrol valve to verify its apaity. The position of this equipment as well as the lenth and size of the pipin that is ahead of the equipment will affet this pressure level, whih in turn will affet the total head of the pump. This artile will show you how to determine the pressure anywhere in any system, whih in turn will allow you to modify that pressure level and understand the impat on the pump. The system onfiuration in Fiure illustrates how drastially the pressure head an vary in a simple pumpin system. The pressure just before the ontrol valve is a parameter required to size the valve. It is alulated by the method desribed in this artile. We will use the ontrol valve as an example but this ould be any piee of equipment. Fiure shows a eneral representation of a pumpin system. The variables z, H and v represent Fiure The pressure variation within a typial pumpin system. the onditions that affet the pump total head at point (the inlet) and point (the outlet of the system). z is the elevation, v the veloity of fluid partiles and H the pressure head. H and H represent the pressure heads orrespondin to the pressures in the tanks p and p. If the tanks are open to atmosphere that H and H will equal zero. It is always possible to alulate pressure head when the pressure is known usin equation [] where SG is the speifi ravity of the fluid. H ( ft.3 p( psi) fluid) = SG []

2 How to alulate pressure anywhere Fiure A eneral representation of a pumpin system. HOW TO CALCULATE THE PUMP TOTAL HEAD FROM THE ENERGY BALANCE An enery balane an determine the total head of the pump or the enery required of the pump. The amount of enery that the pump must supply will be the differene in enery between the eneries available at points and plus the pipin and equipment frition loss in the system at the required flow rate. A very detail explanation of this is available in a book alled Pump System Analysis and Centrifual Pump Sizin by Jaques Chaurette and is available on the web sites The enery balane is: ( pf+ peq) p P ( p p) ( ) ( ) v v = + z z + [] ρ ρ ρ Equation [] is Bernoulli s equation with the pump pressure inrease ( p P ) and fluid frition loss due to pipin ( p F- ) and equipment ( p EQ- ) frition terms added. Pressure an be expressed in terms of fluid olumn heiht or pressure head. H p = ρ [3] All pressure terms in equation [] are replaed by their orrespondin fluid olumn heihts, with the use of equation [3] H p = ρ HF, pf = ρ, et.). The onstant ( ) anels out. The total head of the pump is:

3 How to alulate pressure anywhere 3 H ( ft fluid) = ( H F + H EQ ) + ( v v ) + z + H ( z H ) P + [4] The unit of total head ( H P ) is feet of fluid in the Imperial system and meters of fluid in the metri system. (See the variable nomenlature table at the end of the artile for the meanin of the variables in this artile) CALCULATE THE PRESSURE HEAD ANYWHERE ON THE DISCHARGE SIDE OF THE PUMP Equation [4] is the result of an enery balane between points and. The same proess of makin an enery balane an be applied between any two points for example points and (see Fiure 3). We an do an enery balane between points and point and sine we know the value of the total head H P we an alulate the onditions at point. First, alulate the total head for the omplete system usin equation [4]. Next, a ontrol volume (CONTROL VOLUME ) is positioned to interset point and point (see Fiure 3). Point an be loated anywhere between P and. The system equation (equation [4]) an be used with point as the outlet instead of point. It is then resolved for the unknown variable H x instead of H P. Fiure 3 The ontrol volume determines where the onditions on the dishare side of the pump an be alulated.

4 How to alulate pressure anywhere 4 Equation [4] ives the total head for the omplete system and is repeated here: H P = ( H F + H EQ) + ( v v ) + ( z + H ( z + H ) Equation [4] is applied with the followin hanes: all terms with subsript are replaed with the subsript, H =H, H F- = H F-, H EQ- = H EQ-, v = v, z = z. The unknown term Hx is isolated on one side of the equation and we obtain equation [5]. H H H H v v z H z = P ( F + EQ) + ( ) + ( + ) [5] The unknown pressure head (H x ) an also be determined by usin that part of the system defined by ontrol volume (see Fiure 3) by usin the same reasonin as above, in equation [4], H P = 0 and all terms with subsripts replaed with. Therefore, H =H, H F- = H F-, H EQ- = H EQ-, v = v, z = z The unknown term Hx is isolated on one side of the equation and we obtain equation [6]. H H H v v z H z = ( F + EQ) + ( ) + ( + ) [6] We now have two methods for determinin the pressure head at any loation. We an use one equation to verify the results of the other. The alulation of H is often quiker when usin equation [6]. Note that in equation [6] the value of H P is not required to alulate H x. CALCULATE THE PRESSURE HEAD ANYWHERE ON THE SUCTION SIDE OF THE PUMP We an determine the pressure head anywhere on the sution side of the pump by the same method. In this ase, H P = 0 sine there is no pump within the ontrol volume (see Fiure 4). H P = 0 and subsript is replaed with subsript in equation [4]. The unknown term Hx is isolated on one side of the equation and we obtain equation [7]. H = ( H F + H EQ v ) + ( z+ Hz ) + ( v ) [7] The veloity (v ) must be the same as the one at point in the omplete system. Equation [6] is important in alulatin the N.P.S.H. available and avoidin avitation. You an find an artile that treats this subjet speifially at

5 How to alulate pressure anywhere 5 Fiure 4 The ontrol volume determines where the onditions on the sution side of the pump an be alulated. Let s do a pratial example, suppose you have a piee of equipment that requires 30 psi pressure at its inlet to funtion properly. This has happened to me, the equipment was a Voith Turbo-Cleaner and Voith speified that the leaner needed 30 psi pressure at its inlet. The system is shown in Fiure 5. Fiure 5 A system that requires a speified pressure at the inlet of an equipment. I alulated the total head of the pump usin equation [4] without takin into aount the inlet pressure requirement of the leaner and obtained a value of 70 feet of fluid. You will have to take my word for this, as you do not have enouh information to do the alulation, for example you are missin the pressure drop aross the leaner, the properties of the fluid, et.

6 How to alulate pressure anywhere 6 Usin equation [5], I alulated the pressure head at the inlet of the leaner (point 3) to be 40 feet that orresponds to 7 psi. This is learly smaller than required by the manufaturer. There are several options to orret this, the main ones are:. If the system is in the desin stae, reposition the leaner to inrease the pressure at the inlet. If this is impratial then. Close the manual valve B (see Fiure 5) at the outlet of the leaner (point 4) to inrease the pressure at the inlet (point 3). You annot lose the valve on an existin system that has not been desined for the additional pressure required at the leaner inlet. To do so would redue the flow and that is not aeptable. You must deal with this durin the initial staes of desin or if the installation is already in operation modify the pump. The pressure required (30 psi) at the leaner inlet orresponds to (use equation []) 69 feet of pressure head. Prior to applyin this requirement, I alulated that the pressure head at point 3 was 40 feet, we are missin 9 feet. We must now alulate the total head of the pump that will produe the value of 69 feet at point 3 at the flow rate required. Usin equation [5] and with the value of H (69 feet), we an then alulate the value of H P, the total head of the pump, whih will satisfy the requirements.

7 How to alulate pressure anywhere 7 Symbols Variable nomenlature Imperial system (FPS units) Metri system (SI units) H head ft (feet) m (meter) H P Total Head ft (feet) m (meter) H EQ equipment frition head loss ft (feet) m (meter) H F frition head loss in pipes ft (feet) m (meter) p pressure psi (pound per square kpa (kilopasal) SG speifi ravity; ratio of the fluid density to the density of water at standard onditions inh) non-dimensional v veloity ft/s (feet/seond) m/s (metre/seond) z vertial position ft (feet) m (meter)