Flow Through Pipes

Flow Through Pipes Points : Flow through Pipes chapter, Loss of Head in Pipes, Chezy’s formula for loss of head in pipes , Darcy Formula for loss of head in pipe, Hydraulic Gradient Line Introduction A pipe is a closed conduit, generally of circular cross-section, used to carry water or any other fluid. When the pipe is running full, the flow is under pressure. But if the pipe is not running full (as in the case of sewer pipes, culverts etc.), the flow is not under pressure. In such a case the atmospheric pressure exists inside the pipe. Loss of Head in Pipes When the water is flowing in a pipe, it experiences some resistance to its motion, whose effect is to reduce the velocity and ultimately the head of water available. Though there are many types of losses, yet the major loss is due to frictional resistance of the pipe only. The frictional resistance of a pipe depends upon the roughness of the inside surface of the pipe. It has been experimentally found that more the roughness of the inside surface of the pipe, greater will be the resistance. This friction is known as fluid friction and the resistance is known as frictional resistance.

The earlier experiments on the fluid friction were conducted by ‘Froude who concluded that:
1. The frictional resistance varies approximately with the square of the velocity of the liquid.
2. The frictional resistance vanes with th nature of the surface.

Later on, some experiments formulae were derived for the loss of head due to friction, out of which the following two’ are important from the subject point of view:
1. Darcy’s formula for loss of head in pipes, and
2. Chezy’s formula for loss of head in pipes Chezy’s formula for loss of head in pipes

Darcy Formula for loss of head in pipe

Hydraulic Gradient Line If pressure heads (i.e., p/w) of a liquid flowing in a pipe be plotted as vertical ordinates on the centre line of the pipe, then the line joining the tops of such ordinates is known as hydraulic gradient line (briefly written as H.G.L.)

If the sum of pressure heads and velocity heads (P/w + V2/2g flowing m a pipe be plotted as vertical ordinates on the centre line of the pipe, then the line joining the tops of such ordinates is known as total energy line (briefly written as T.E.L.)

Or, in other words, the total energy line lies over the hydraulic gradient by an amount equal to the velocity heads.

Note : The above mentioned two lines give very useful information regarding the flow of liquid in the pipeline. Some of them will be discussed in the following pages.