Question

Explain the terms Hydraulic Grade Line and Total Energy Line. Compare the total energy line and hydraulic grade lines for the pipe sections if there is sudden enlargement in the pipe section or sudden contraction in the pipe with the help of sketches.

Answer 1

Hydraulic gradient line and total energy line represents the various heads of a flow through a pipe. For both these lines, some reference line is chosen.

Hydraulic gradient line (HGL) may be defined as " a line which represents the sum of pressure head and datum head of a fluid flowing through a pipe w.r.t the datum." Or, we can say this line joins the points representing the values of piezometric heads at the various cross sections of the pipe in the pipe flow.

Total energy line (TEL) is defined as " the line which represents the sum of pressure head, datum head and kinetic head of a fluid flowing a pipe w.r.t the datum." Or, we can say this line joins the points representing the values of total head at the various cross sections of the pipe in a pipe flow. It is also known as​​​​​ Energy grade line (EGL).

The hydraulic gradient line will always lie below the total energy line.

Following figure shows the energy lines for an inclined pipe running between two reservoirs.

We must keep in mind that, the total energy line will always go down in the direction of flow until or unless some external energy is supplied, whereas the hydraulic gradient line may go up or down in the fluid flow.

In a uniform diameter pipe, HGL will always be parallel to TEL. The vertical gap between these two lines at any section of the pipe represents the value of kinetic head.

Case of sudden enlargement in pipe

Due to sudden enlargement in pipe, there will be an enlargement loss. As a result, there is a sudden fall in TEL in the direction of flow.

Also, the hydraulic gradient line will rise in the direction of flow when there is a flow from smaller dia pipe to larger dia pipe. This is because, the velocity in larger pipe is less than that of narrower pipe. Hence the vertical gap between TEL and HGL will reduce. Or we can say, piezometric head in larger pipe will be more (as pressure head increases in larger pipe) than that in narrower pipe. Hence, HGL rises suddenly.

Case of sudden contraction

Due to sudden contraction in pipe, there will be a contraction loss. As a result, there is a fall in TEL.

As the fluid flows from larger dia to smaller dia pipe, velocity of flow increases and pressure head decreases. Therefore, the vertical gap between energy lines will increase. Or we can say, as there is a reduction in piezometric head in narrower pipe and hence, HGL further falls down.