27 / 40
loss plus static head loss, using Bernoulli’s Theorem of the
Law of Conservation of Energy where h
p
= (Z
b
– Z
a
) + ∑h
L
In our case, with a 2” diameter hose,
f
= 0,19
The slurry flow will give a friction loss of about 8,4 m
The Dynamic head on the pumps is then 8,4 + (3 – (-5))
= 16,4 m
Minus 5 m the suction height and 3 m being the discharge
height.
Pump selection
From the previously mentioned brochure, we can locate the
preliminary pump size from the location of the Discharge
rate of 4,75 L/sec and total head of 16,4 m as being a
2/1,5 B-AH slurry pump.
From the pump curve we can read off the Net Positive
Suction Head (NPSH
a
). We should now revisit the line losses
due to new fittings being introduced, eg, the 1,5” pump out-
let which will be enlarged to pipe size, but for our purposes
this will be ignored. While the selection seems adequate,
the small outlet diameter may be a problem with gravel. A
larger pump and increased production can be calculated
to allow a larger outlet pump size.
Equivalent water dynamic head
From theWeir Manual’s ‘Head ratio to efficiency ratio curves’
we can read off the HR/ER for and find HR/ER = 0,95
The equivalent head of water is therefore 16,4/0,95 = 17,26
of water.
Using a pump efficiency of 70 % from the pump curve,
we can calculate the power required to drive the pump
Brake HP = (gρ/1 000 x Q x h
p
) / eff = (9,81 x1 140/1 000 x
0,00475 x 17,26) / 0,7 = 1,31 kW.
Q = m
3
/sec , 1 000 = W/kW, h
p
= head loss in m, eff the
efficiency of the pump.
We would probably use a 4,5 kW diesel engine.
NPSH required at pump intake to avoid
cavitation
The NPSH required at any point on the pump curve is the
minimum net amount of energy of the actual mixture being
pumped above absolute zero pressure that the fluid must
have at the entrance to the impeller to avoid cavitation.
Slurry pumps fortunately do not exhibit the complete fall
off of the flow that classical water pumps exhibit when the
point is reached on the curve where cavitation commences
due to the high flow rate and consequential line losses. This
is most probably owing to the use of wide impellers and the
fact that vapour bubbles do not form across the whole width
of the impeller. The net positive head (NPH) at a point in the
pipeline is the absolute pressure head at that point, plus the
velocity head, less the vapour pressure. Reading a gauge
at a point in a pipeline, the NPH would be the gauge head
reading, plus atmospheric pressure head, minus the fluid
vapour pressure head, plus the velocity head. At the suction
inlet of the pump this is referred to as the NPSH and the
minimumNPSH required to avoid cavitation is shown on the
performance curve as NPSH required or NPSH
r
.
Net positive suction head available or
NPSH
a
To avoid cavitation (the phenomenon of formation of vapour
bubbles of a flowing liquid in a region, where the pressure
of the liquid falls below its vapour pressure), it is important
to compare the required NPSH (Net Positive Suction Head)
to the available NPSH.
From the system conditions and the liquid being pumped,
we can calculate the NPSH
a
and this must exceed the NPSH
r
to avoid cavitation. In practice, we are trying to avoid the
creation of vapour bubbles due to the pressure at the im-
peller being lower than the vapour pressure of the liquid,
which then creates bubbles.
NPSH
a
= H
atm
– H
vap
– Z
s
– H
i
– H
fs
H
atm
= Atmospheric pressure expressed in
metres of slurry
H
vap
= Absolute vapour pressure of the liquid
slurry carrier in metre of slurry
Z
s
= Static suction head, ie, the vertical height
PUMPS &
VALVESWW
25
Chemical Technology • April 2016