Lesson 8 - Control of Fluid Flow 1

In the same way that we can assess the performance of a car in many different ways, e.g. top speed, time to go from 0-100 km/h, litres of fuel per 100 km etc., we can assess the performance of a pump in a number of different ways too. When comparing the performance of a sports car with that of a family saloon, or one pump with another pump, it is important to bear in mind whether they are fit for purpose. To make such a comparison, we need to match a set of performance criteria against the required job and outcome. First, we must define the performance of a pump.

Performance criteria

There is a multitude of performance criteria to describe and assess the performance of a pump, and there is not enough time to cover all the subtleties here. A pump specification sheet, generally provided by a pump manufacturer, would give the various criteria, so let us consider four of the major ones:

• Capacity

• Total head

• Pumping power

• Efficiency

Let us look at each of these in more detail.

Capacity Q

In the same way that the capacity of a beer bottle is the volume the bottle can hold; the capacity of a pump is the flow rate of the pump. Simple enough? Well, not quite, as the flow rate through a pump can be changed (as we will see a little later), so one should be clear about under what condition the pump is running when it is delivering the specified capacity. We will expand on this in due course.

Total head ∆P

Head, as a representation of pressure, is not new to us as we covered it previously. However, ‘total head’ is a new term. Simply put, total head is the total pressure which a pump can generate between its inlet and outlet. You can think of this as the pressure lift or increase that the pump can generate.

It is usually expressed as a head in metres of water, so we must be careful to account for the use of another liquid with a different density.

Pumping power P_p

Pumping power (measured in watts W) is defined as the power required to pump the liquid at a capacity against a total head, or in other words, the power absorbed by the liquid from the pump when passing through the pump. It is defined as the product of the capacity Q (m³/s) and the total head ∆P (Pa):

Pumping power is the power absorbed by the liquid during pumping. It should not be confused by the power drawn by the electric motor that drives the pump. This would include other mechanical and electrical losses through the motor and frictional losses in the pump itself, in addition to pumping power.

Let us do a worked example on determining pumping power. 

Determine the pumping power for a wort pump if the capacity is 1,000 hL/h and the total head is 30 m water (water density is 998 kg/m³).

We know that pumping power is given by:

But we need the capacity expressed in m³/s rather than hL/h, so:

And we need the total head ∆P to be in Pa and not metres of water, so we will convert using the following:

The pumping power is given by:

Efficiency η

Pump efficiency is an extension to the previous key point on pumping power as there are a number of power losses between the (electrical) power being supplied and the power being absorbed by the liquid. These losses would be within the pump motor and the pump’s internal workings. No machine is 100% efficient – there are always losses. These would include:

• Electrical losses within the motor

• Mechanical losses within the motor’s bearings

• Mechanical losses within the pump’s seals, bearings, and gearbox (if used)

The effect of these losses is to increase the power drawn by the pump’s motor to achieve a particular pumping power. To account for this, we use the concept of efficiency η (the Greek symbol eta pronounced ‘e-ta’) which is defined as the ratio of pumping power P_p to that drawn by the pump’s motor P_m:

We should note that efficiency does not have any units as they cancel out on the top and bottom of the equation. Often, we will see a percentage unit used and, in this case, the efficiency figure, as described, has been multiplied by a factor of 100.

Pump efficiency η is not a constant for a particular pump and we will soon see that it varies depending on capacity and total head; but, for a centrifugal pump, for example, it can vary from 0.9 down to 0.5. If η was equal to 0.5, then for every watt we require for pumping power, another watt is lost, but we pay for both watts. This is not an appealing situation so we will consider efficient operation of pumps in the next section.

Let us do a worked example dealing with pump efficiency.

A pump is running with a pumping power of 8,158 W. If the pump efficiency at that condition is 75%, what is the electrical power drawn by the pump motor?

We know that pump efficiency is defined as:

So, rearranging for the electrical power drawn by the motor gives:

(You did remember to convert the percentage efficiency to a fractional efficiency, didn’t you? i.e. 75 % → 75/100 → 0.75.)

The specifications of capacity, total head, and pump efficiency, and their variations are available for most pumps from the particular pump manufacturer. Correctly interpreting these specifications is important for a brewer to ensure that the pump being considered will do the job required of it.

Let us now have a look at the operating characteristics of one of the workhorses of the brewing industry; the centrifugal pump.