PUMP POWER:

The total work done by the pump, neglecting the losses within the pump itself, will be proportional to the equivalent head difference between the points of suction and discharge. This is known as total head.

H      = H_fs   + H_fd + H_vap     + H_sd     ± H _s

Where,

H_fs= friction head in suction

H_fd = friction head in discharge H_vap = Vap. pressure head

H_sd = discharge head

H_q = Suction head

The power absorbed by the pump, P then becomes,

P_a = QxH_tot xW\ K

Where,

P_a = Power absorbed (kw)

Q = Quantity delivered in litres/sec.

H_tot = Total head in metres.

W = density of liquid in gm/ml (1 for fresh water)

K = 101.9368 (= 102) a constant.

The input power Pin  to the pump required from the prime mover is

Pin = Pa x1\Pump efficiency

For an electrically driven pump, the power consumed is

= Pin  \ Pump efficiency x motor efficiency  in kw

Generally, suction heads require to be greater for high speed or large capacities than for low speeds or small capacities. Before liquid can flow into a pump, the air or vapour in the suction line must be evacuated sufficiently to cause the liquid to flow into the suction chamber. Some pumps (known as self - priming pumps) do this automatically when they are started. In others, special priming devices must be used to withdraw the air and lower the pressure in the pump sufficiently to cause flow.

FRICTION LOSSES :

The sum of friction losses depends upon the sectional area and the internal conditions of the pipes and fittings, the velocity and viscosity of the liquid being pumped and the friction caused by bends, valves and other fittings. Frictional resistance to the flow of water varies approximately as the square of the velocity. Thus if the frictional resistance of a condenser and system of piping is equivalent to a head of 5 m when flow is 800 lit/s, the frictional resistance would rise to 5 x 1.5² = 11.25 m with 1200 lits/sec (=800 x 1.5) flow and to 20 m with 1600 lit/s. Tables are provided by pump manufacturers to find the head in metres required to overcome the friction of flow in pipes of different materials and size.

The general law of frictional resistance due to flow of water in a straight circular pipe running full of water may be expressed accurately enough for practical purposes as

             KLV²                             area of pipe bore  D

Hm =---------    if R =------------------------------

          2GR                  wetted perimeter   4

                    KLV²

or,Hm =---------

               2GD  

Where,

Hm =Head loss (-m) due to friction.

L = length of pipe (m)

V = Speed of flow (m/s)

D = Bore of pipe (m)

G = Gravitational Constant = 9.81 m/sec²

To this must be added the loss due to bends each equivalent to from 3 to 6 m of straight pipe, depending upon the radius of bend. Tables are provided by manufactures to find losses due to  bends and fittings.

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