We were discussing the basics of reciprocating
pump, main
components of a reciprocating pump and working principle of reciprocating pump in our recent posts.
Today we will start here with the ideal indicator
diagram of reciprocating pump and we will also find out here the importance of ideal
indicator diagram of reciprocating pump to determine the work done by
reciprocating pump with the help of this post.
Ideal indicator diagram of reciprocating pump
Ideal indicator diagram of reciprocating pump is basically
a graph between the absolute pressure head in the cylinder and the distance travelled
by the piston from inner dead centre for one complete revolution of the crank.
As the maximum distance travelled by the piston will
be equal to the stroke length and hence we can also say that ideal indicator
diagram of reciprocating pump will be basically a graph between the absolute
pressure head in the cylinder and stroke length of the piston for one complete
revolution.
As we know that volume of water delivered in one
revolution will be the product of area of cross section of the piston or
cylinder and length of stroke i.e. V = A x L
Where, cross sectional area of the piston or cylinder
will be constant and therefore volume of water delivered in one revolution will
be directionally proportional to the length of stroke i.e. V α L.
Therefore, ideal indicator diagram of reciprocating
pump could also be considered as graph between the absolute pressure head and
volume for one complete revolution of the crank.
Let us draw here first the ideal indicator diagram of reciprocating pump and then we will understand this diagram in detail.
Following figure, shown here, indicates the
reciprocating pump.
Where,
Hatm = Atmospheric pressure head
L = Length of stroke
hs = Suction head or vertical height of the
cylinder axis from the water surface in the sump
hd = Delivery head or vertical height of
delivery point from the cylinder axis
As we have recently discussed that the graph between the
absolute pressure head in the cylinder and stroke length of the piston for one
complete revolution will be the ideal indicator diagram of reciprocating pump.
Therefore, absolute pressure head will be taken as
ordinate and stroke length will be taken as abscissa as displayed here in
following figure.
Following figure indicates the ideal indicator diagram
of reciprocating pump, where line EF shows the atmospheric pressure head.
In ideal case, if we neglect the velocity and
acceleration of fluid in cylinder piston and suction pipe, the suction pressure
should be sufficient enough to lift the liquid i.e. water by a vertical height hs.
Therefore, suction pressure head will be equal to the
vertical depth hs. In ideal case, the pressure head inside the
cylinder will be constant throughout the process of suction stroke where piston
moves towards outer dead centre.
Therefore, AB line will indicate here the suction
stroke and it will be below than the atmospheric pressure head EF as displayed
in above figure.
At the end of suction stroke, piston will push the
liquid i.e. water. If we assume the liquid as fully incompressible, there will
be instant increase in pressure of liquid as soon as piston will push the
liquid.
Because, if we recall the property of a fully
incompressible liquid, liquid will be pressurised instantly without change in
volume. BC line shows the instant pressure rise of liquid up to delivery
pressure head when piston will push the liquid at the end of suction stroke.
CD shows the delivery stroke in above figure. During
delivery stroke, the pressure head in the cylinder will be constant and will be
equal to the delivery head hd and it will be above the atmospheric
pressure head by a height of hd as displayed in above figure.
Total static lift of the pump will be hs + hd.
Similarly, at the end of delivery stroke when piston
will come to inner dead centre, there will be instant pressure drop when piston
start to move towards outer dead centre. This instant pressure drop, when piston
start to move towards outer dead centre, is shown by DA in above diagram of reciprocating
pump.
Therefore, for one complete revolution of the crank, pressure
head in the cylinder will be indicated by the diagram A-B-C-D-A. This diagram
is known as ideal indicator diagram of reciprocating pump.
As we have already seen, in ore previous post, that
work done by the reciprocating pump per second will be given by following
equation as mentioned below.
Work done by the reciprocating pump = ρ g A L N x (hs
+ hd) / 60
Work done by the reciprocating pump = K x L x (hs + hd)
Because, ρ g
A N / 60 = Constant = K
Therefore, we can say
that
Work done by the reciprocating pump = K x AB x BC
Work done by the reciprocating pump = K x Area of indicator diagram
Because,
Length of stroke L = AB
Total static lift of the pump will be hs + hd = BC
Therefore, we have seen here the ideal indicator
diagram of reciprocating pump and also we have concluded that work done by the
reciprocating pump will be directly proportional to the area of indicator diagram.
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Further we will find out, in our next post, effect of acceleration and friction on indicator diagram of reciprocating pump.
Reference:
Fluid mechanics, By R. K. Bansal
Fluid machines, By Prof. S. K. Som
Image courtesy: Google
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