Calculating Head Pressure Loss
Calculating head height and pressure loss is crucial when designing pumping systems and creating pump specification sheets for quote/tender requests.
In the world of pumps and fluid dynamics, we talk a lot about “static head”, “friction head”, and “dynamic head” pressure. Here, we go back to basics and take it step-by-step to unpack what these terms mean;
What is Head Pressure?
When designing pipeline systems and specifying pumps, one of the most important factors is the head pressure required, put simply: how much pressure the pump needs to exert on the fluid to move it from A to B.
Although pressure itself is measured in psi or bars, head pressure is measured in ‘height equivalent’ metres (or feet) – the difference in elevation between system inlet and discharge.
Static Head
Here is a water tower:
The vertical distance between the top of the stored water and the bottom of the column is 25m. We can say that the water pressure (bar or PSI) at the base of the tower is equivalent to 25m Head Pressure.
Setting aside energy loss through friction forces, the 25m of head pressure generated is enough to propel the water upwards by 25m.
This gravitational system produces 25m of head pressure, at the centre-line of the discharge pipe.
As the water level in the header tank drops, so does the pressure head generated – which is why the resulting fountain will also decline in height. To maintain our fountain’s height, we have to keep the tank level topped up constantly at 25m of head, and to exceed 25m fountain height we would need to add additional pressure; i.e. install a pump.
This means a pump capable of 25m head pressure would, in theory, produce a fountain of that height. Theoretically, the height of the fountain is only limited by the force of gravity, which gradually reduces the vertical flow to zero. The point at which this happens is called the “shut-off” head.
It’s worth mentioning here about a key difference between centrifugal pumps and positive displacement pumps. Centrifugal pumps add head pressure to the existing inlet pressure (“suction head”), making the distance between the pump and shut-off head dependent on the tank water level. Positive displacement pumps work independently of inlet pressure, making their shut-off height easier to predict.
Friction Head
So far, we have ignored friction loss in our theory. However, in reality, energy will be lost due to friction from the discharge nozzle and any pipework involved.
As a real-life example of this, the Emperor fountain at Chatsworth House in Derbyshire makes an interesting study – predating the invention of the centrifugal pump, it is the world’s highest gravity-powered fountain. Its head height has been recorded at 90m, although system wear and debris buildup have increased friction loss and today it achieves around 60m maximum head.
This head pressure is achieved through a 122m height difference from the reservoir surface down to the fountain in the valley below, showing the significant effect that friction has on the total achievable head.
In order to achieve our desired total head (which in our Chatsworth case study, had to exceed Emperor Czar Nicholas’ best fountain height), we need to add some compensating “Friction Head” to our measured “Static Head” requirement.
As dynamic head is the sum of two things – static head and friction head, it is often referred to as “total dynamic head” or TDH.
Elevation height + head pressure loss = Total Dynamic Head (TDH)
Total Dynamic Head (TDH)
This is where things get…well pretty dynamic!
Whereas measuring the elevation difference (static head) is straightforward, head pressure loss calculations can get rather more complex. Unlike our fountain examples, fluid transfer pumps usually have to contend with the friction and turbulence of multiple bends, valves, and pipe connections.
There are multiple factors that impact friction loss, but to keep this simple for now here are the 5 most significant practical factors:
- Length of pipe.
- Diameter of pipe (mm). Wider pipes reduce friction (and reduce the velocity).
- Velocity of flow (m/s). This is determined by the flow rate and the pipe’s internal diameter. Higher velocity increases friction.
- Number of bends and their severity. Bends distort the flow, which tends to split into two opposing spiral flows, causing a pressure loss.
- Inline components (valves, sensors, etc.). The manufacturer can provide the ‘K’ friction factor value for each item.
As the water flows against the pipe wall, it experiences some friction - not a lot if the pipe is straight and smooth - but much more if there are bends in the system and the pipe material is roughly textured. Different types of pipe material have a known friction factor, e.g. Gromatex armoured hose, often used for abrasive slurries, has a lower friction factor than cast iron, but a greater one compared to smoother plastic piping.
Because most friction occurs against the wall of the pipe, a wider diameter has a greater volume-to-surface ratio, causing less friction.
Industrial pump systems generally get very complex, with various valves, flow meters, testing probes, and bends adding more friction.
The longer the fluid flows through the pipework, the overall friction resistance increases – meaning we have to factor pipe length into our calculation of friction loss.
All this friction causes a loss of head pressure, reducing our original ‘fountain height’. In order to achieve our original height, we must factor in these losses. This is called “total dynamic head” and should be used alongside flow-rate when selecting the best pump for the duty.
When using a centrifugal pump, there is a subtle difference between physical shut-off head and TDH quoted for the pump. The TDH is the distance between the surface of the source fluid and the shut-off head, so as the supply level rises and falls, so does the physical shut-off head.
Pump working fine when tank is full (high suction head pressure)
Pump deadheads (shut-off head reached) when tank level drops. Note: TDH has remained the same, but the suction head has reduced
Pump deadheads (shut-off head reached) when tank level drops. Note: TDH has remained the same, but the suction head has reduced
Therefore, measure your required head height requirements based on your minimum expected source level.
Our pump engineers calculate head pressure loss when designing systems for clients, but if you want to figure out things for yourself, various online calculators can give you an estimate of the head pressure loss to expect in your system.
Final Terminal Pressure
At the point of discharge, some end terminal pressure at the point of discharge will ensure the pump doesn’t deadhead (reach its shut-off head before discharging from the system). With most dewatering projects, the water can flow into a holding tank or lagoon at low pressure, however, many industrial processes require water delivery at a certain pressure, for instance, wash plant or filter-press feeds.
As a general rule of thumb, add 10 metres of “head height equivalent” for each 1 bar of pressure you require at the pump discharge point.
Hopefully this gives you a better idea of what information would be relevant when specifying a pump for an existing system, and provides an insight into pump system design for efficiency and effectiveness.
Reach out to our engineering and technical sales department for help with your pump system projects.
