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53. Suppose that a mass
Δ
m
of water is pumped in time
Δ
t
. The pump increases the
potential energy of the water by
Δ
mgh
, where
h
is the vertical distance through which it is
lifted, and increases its kinetic energy by
2
1
2
mv
Δ
, where
v
is its final speed. The work it
does is
2
1
2
Wm
g
h
m
v
Δ=
Δ +Δ
and its power is
2
1
.
2
Pg
h
v
tt
ΔΔ
§·
==
+
¨¸
©¹
Now the rate of mass flow is
Δ
m
/
Δ
t =
ρ
w
Av
, where

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