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# Hydraulic Calculations and Fluid Mechanics

Chapter 9 of the book deals with hydraulic calculations, the practical relative of fluid mechanics, for both compressible and incompressible fluids.

“*I am an old man now, and when I die and go to Heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics and the other is the turbulent motion of fluids. And about the former I am rather more optimistic.” **– Sir Horace Lamb*

At university, all chemical engineers study fluid mechanics, which is a kind of applied mathematics, usually combined with a bit of applied dishonesty.

The truth is that no one really understands the turbulent motion of fluids, or can predict it with a high degree of precision. Consequently even the most basic fluid mechanics courses have to handle a transition from first principles mathematics to the rough heuristic of the Moody diagram.

This is the point where an honest lecturer should admit we can’t actually use Bernoulli’s equation to solve any useful problems, and we are consequently bringing in a chart based on empirical relationships determined by experiment to fill the gaps in our understanding with a fiddle factor.

Not all lecturers are so honest or insightful and students may leave university thinking that they understand something which no one does – until someone asks them to size a pump.

Hydraulics is the more practical cousin of fluid mechanics, which we mainly use to specify pump and equipment sizes as accurately as required for practical purposes. Engineers don’t have to completely understand things in order to exercise sufficient control to achieve a given aim…

A notable omission from university courses is an understanding of how to read a pump curve, which is an essential requirement to do what we are probably going to do with the head/flow pairs we calculated across the design envelope.

The most frequent use of pump curves is for the selection of centrifugal pumps, as the flow rate of these varies so dramatically with system pressure. Pump curves are used far less frequently for positive displacement pumps.

A basic pump curve plots the relationship between head and flow for a pump at a given supply frequency. On more sophisticated curves, there may be nested curves representing the flow/head relationship at different supply frequencies or rotational speeds, with different impellers, or different fluid densities. The pattern is that curves for larger impellers or faster rotation lie above smaller impellers or slower rotation, and lower specific gravity above high for centrifugal pumps.

Let’s start with a basic curve:

Along the horizontal axis we have increasing flow (Q), and along the vertical axis, increasing pressure (H). The curve shows the measured relationship between these variables, so it is sometimes called a *Q/H curve*. The intersection of the curve with the vertical axis represents the *closed valve head* of the pump. These pumps are generated under shop conditions and ideally represent average values for a representative sample of pumps.

We can use our calculated flow/head pairs to plot a system head on the same axes, and see where our system head meets the Q/H curve. This will represent the operating or *duty point* of the pump.

We will have a system head curve for the expected range of flows at a given system configuration. Throttling the system will give a different system curve. We will need to produce a set of curves which represent expected operating conditions, generating a set of duty points.

That’s it as far as our basic curve is concerned, but it is common to have efficiency and motor rating curves plotted on the same graph, (but not the same vertical axes) as in the example below.

So we can see that we can draw a line vertically from the duty point to the efficiency curve, and obtain the pump efficiency at the duty point by reading the vertical axis at the point of intersection. Similarly we can draw a vertical line to the motor duty curve, and obtain a motor power requirement….”

The chapter also covers how to match calculation rigor to stage of design, handle networks of pipework and fittings, deal simply with compressible fluids, and many other aspects of hydraulic design which early stage designers find difficult.

**Read more from Sean on SciTech Connect**

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**About the Author**

Professor Moran is a Chartered Chemical Engineer with over twenty years’ experience in process design, commissioning and troubleshooting. He started his career with international process engineering contractors and worked worldwide on water treatment projects before setting up his own consultancy in 1996, specializing in process and hydraulic design, commissioning and troubleshooting of industrial effluent and water treatment plants.

In his role as Associate Professor at the University of Nottingham, he co-ordinates the design teaching program for chemical engineering students. Professor Moran’s university work focuses on increasing industrial relevance in teaching, with a particular emphasis on process design, safety and employability.

Connect with Sean on LinkedIn here, check out his Facebook page here and stay up-to-date on his thoughts, research and practice at his personal blog here.

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