# HYDRAULIC GRADIENT LINE (HGL) AND TOTAL ENERGY LINE (TEL)

Consider a long pipe line carrying liquid from a reservoir A to reservoir B. At several points along the pipeline let piezo meters be installed.

The liquid will rise in the piezometers to certain heights corresponding to the pressure intensity at each section.

The height of the liquid surface above the axis of the pipe in the piezometer at any section will be equal to the pressure head (p/w) at that section.

On account of loss of energy due to friction, the pressure head will decrease gradually from section to section of pipe in the direction of flow.

If the pressure heads at the different sections of the pipe are plotted to scale as vertical ordinates above the axis of the pipe and all these points are joined by a straight line , a sloping line is obtained, which is known as Hydraulic Gradient Line (H.G.L ).

Since at any section of pipe the vertical distance between the pipe axis and Hydraulic gradient line is equal to the pressure head at that section, it is also known as pressure line

Moreover if Z is the height of the pipe axis at any section above an arbitrary datum, then the vertical height of the Hydraulic gradient line above the datum at that section of pipe represents the piezometric head equal to (p/w + z). Sometimes the Hydraulic gradient line is also known as piezometric head line.

At the entrance section of the pipe for some distance the Hydraulic gradient line is not very well defined. This is because as liquid from the reservoir enters the pipe, a sudden drop in pressure head takes place in this portion of pipe. Further the exit section of pipe being submerged, the pressure head at this section is equal to the height of the liquid surface in the reservoir B and hence the hydraulic gradient line at the exit section of pipe will meet the liquid surface in the reservoir B.

If at different sections of pipe the total energy ( in terms of head) is plotted to scale as vertical ordinate above the assumed datum and all these points are joined, then a straight sloping line will be obtained and is known as energy grade line or Total energy line (T.E.L)

Since total energy at any section is the sum of the pressure head (p/w), datum head z and velocity head 𝑉2/2𝑔 and the vertical distance between the datum and hydraulic grade line is equal to the piezometric head (p/w + z), the energy grade line will be parallel to the hydraulic grade line, with a vertical distance between them equal to 𝑉2/2𝑔 at the entrance section of the pipe there occurs some loss of energy called “Entrance loss” equal to 0.5x 𝑉2/2𝑔 and hence the energy grade line at this section will lie at a vertical depth equal to 0.5x 𝑉2/2𝑔 below the liquid surface in the reservoir A. Similarly at the exit section of pipe, since there occurs an exit loss equal to hL = 𝑉2/2𝑔

.The energy gradiant line at this section will lie at a vertical distance equal to 𝑉2/2𝑔 above the liquid surface in the reservoir B. Since at any section of pipe the vertical distance between the energy grade line and the horizontal line drawn through the liquid surface in reservoir A will represents the total loss of energy incurred up to that section.

If the pipe line connecting the two reservoirs is horizontal, then the datum may be assumed to be along the pipe axis only. The piezometric head and the pressure head will then become the same.

If a pipe line carrying liquid from reservoir A discharges freely in to the atmosphere at its exit end, the hydraulic grade line at the exit end of the pipe will pass through the centre line of the pipe, since the pressure head at the exit end of the pipe will be zero (being atmospheric).

The energy grade line will again be parallel to the hydraulic grade line and it will be at a vertical distance of  𝑉2/2𝑔 above the Hydraulic grade line