The genesis of the myth that pumps produce flow, not pressure, lies in the very construction of hydraulic pumps used for motion control applications. They are positive displacement, meaning that for each revolution of the input shaft, a fixed amount of fluid is transferred from the inlet port to the outlet port, internal leakage notwithstanding. This is true for all construction types, that is, gear, vane, piston, abutment, etc.

1. Pumps pump flow, not pressure. |

It follows that if the shaft is turned at a uniform rotational speed, there will a steady, or constant, output flow rate. It is further argued that if there is no restriction at the pump outlet, there will be no pressure, but yet there is flow. The pressure comes as a consequence of some restrictive load. Therefore, the pump generates flow, not pressure. Although it is hard to argue with this thought process, I maintain it is intellectually confining.

**Dealing with reality**

The constraining nature of such thinking was seen a while ago where several grown men, communicating through one of the webbased forums, argued over the pressure pump versus the flow pump for the better part of a year. Such arguments are as worthwhile as arguing the virtue of the chicken having come before the egg. The more glib among them may have won the debate. However, it did nothing to reveal the basic truth and reality of pumping mechanisms. Such discussions are more rightly carried out in a religious forum, not a technical one. Let me shine a more fundamental light on what a pump does.

The National Fluid Power Association (NFPA) defines a pump as a device that converts mechanical input power into hydraulic output power. ISO/DIS 5598 defines a hydraulic pump as “a component that transforms mechanical energy into hydraulic energy.” Note that both address the power or energy conversion function. In complementary fashion, motors convert hydraulic input power into mechanical output power. In fact, most hydraulic fluid power motors will operate as pumps and vice versa. The power or energy conversion concept is more fundamental than the positivedisplacement principle. In fact, the power conversion concept allows gaining a comfort with any pumping mechanism, even the non-positive displacement types, such as centrifugal pumps.

Returning to the positive-displacement pump that is turning and displacing fluid throughout each revolution of the input shaft, it was said that there could be, in concept, flow without pressure. Yes, in some idealized, frictionless world. However, there will never be flow without some pressure in any real-world scenario. The pressure may be low, but it will never be zero. In fact, the pressure and flow will arise and exist simultaneously! As soon is there is fluid in motion, there must also be a commensurate friction-induced pressure.

**Pressure and flow**

On the other hand, it is possible to have pressure with absolutely **no flow**, even in the real world. Such a system can be seen in your home water system. If you put a pressure gauge in one of your water pipes, it will register some pressure, perhaps 45-55 psi. Yet, you can shut off all your faucets, and there will be no flow, but the pressure remains. Hydraulic accumulators can also provide pressure without flow, because of the energy stored in the compressed gas.

In the positive-displacement pumping system, the flow primarily depends on the pump shaft’s speed. These are called p*ump controlled, or pump flow limited* systems, and we generally approach them by concentrating on the rate at which fluid flows.

But the pump does not regulate the flow in the home water system, so we need a different means of determining flow rate. Flow rate depends on the pressure and the flow coefficient of the water faucets, which depend on the degree of opening. These systems are referred to as p*ressure-controlled, or constant pressure systems*, and their analyses cannot be approached from the standpoint that there is a known pump output flow. We need to have knowledge of the pressure and valve coefficients. Knowledge of the pump’s operational capacity is of little or no value.

When the prime mover powers the pump, the energy conversion process begins at the very onset of shaft rotation. Input speed and torque, the constituent parts of input power, and pressure and flow, the constituent parts of output power, all occur simultaneously! It is impossible to say which came first. However, when using mathematical models of pumps and motors, it is not necessary to know which variable came first; it is only necessary to apply the models correctly!

**Relevance to modelling**

Recently, I submitted a first draft of a proposed standard set of mathematical models to the NFPA’s Pump and Motor Committee, T3.9. There are four different models, each with its own set of assumptions and limitations. The models describe both pumps and motors mathematically. Anyone interested in knowing more is urged to contact the NFPA and ask to participate in the development of standard math models for pumps and motors. Below is a brief summary of the four models:

**Zero degree models:** Characterized by having displacement, but no frictional or internal leakage losses. These are *ideal machines*, and, having no losses, have 100% efficiencies. Industry and academia have long referred to these as being “theoretical” models of a pump, an adjective that adds to confusion, not clarity.

**First degree models: **Characterized by having displacement and linearized frictional and internal leakage losses.

**Second degree models:** Characterized by having displacement and linearized frictional and internal leakage losses, but the internal leakages are separated into their port-to-port and port-to-case drain components.

**Third degree models:** Characterized by having displacement and non-linear friction and internal leakage losses, and the extent and complexities of the nonlinearities are left to the discretion of the user of the models.

Needless to say, the First, Second, and Third Degree models are not ideal. They have losses, and, therefore, efficiencies of less than 100%. Although arguable, the trend is toward a progressively more realistic characterization of real-world machines from the Zero Degree models to the Third Degree models. However, no math model can be so detailed as to perfectly emulate real world in totality. Models can only be close approximations to real machines.

Here is the important point: When the energy conversion process of the pump is modeled in a more-or-less realistic way, it is possible to start by knowing the flow — or, just as easily, we can start with knowing the pressure. The other variables are calculated, and we care not which, if any, came first. The proposed models provide the flexibility needed to characterize, design and analyze the most complex systems of an increasingly automated industrial world.

**Evaluating concepts**

Accepting the concept of a pump or motor as being an energy converting device allows throwing the shackles off the flow-pumping or pressure-pumping argument. So will accepting mathematical models as a means of “explaining” what the machine is doing under any operating scenario. Then the real problems of determining the adequacy of a pump or a motor to a particular application can be addressed. What will the machine do in an application? That’s the important question. Energy conversion and math modeling will lead to useful answers to that question.

Why are such concepts important? Mostly, they help expand our mental boundaries, but also, the idea that pump output flow is a dependent, not independent variable, is foreign. If all the flow from a positive-displacement pump in a system is directed to, say, a cylinder, the speed of the cylinder is governed by that flow and the cylinder dimensions. The cylinder load has minimal effect.

On the other hand, consider a system with a pressure-compensated pump (nominally, a constant-pressure source) and a proportional valve connected to a cylinder. The speed of the cylinder will be governed by the pressure of the pump’s compensator setting, the degree of opening of the valve (its flow coefficients) the size of the cylinder, and the load on the cylinder.

In this instance, it is far more advantageous to view the pump as what it is, a pressure source, and let the flow take on the value that satisfies the model of the system. The calculations are more complex than with pump flow controlled systems. However, knowing the pump’s speed and displacement does not comprise a useful starting point. Flow and displacement become a consequence of the aforementioned settings and parameter values.