Very Hard Physics Problem Please Help?
Tuesday, October 13th, 2009 at
10:03 am
A fountain designed to stray a column of water 7 m into the air has a 2 cm diameter nozzle at ground level. The water pump is 2.6 m below the ground. The pipe to the nozzle has a diameter of 4 cm. Find the necessary pump pressure.
Tagged with: Hard • Help • Physics • Please • Problem • Very
Filed under: Water Fountain Pumps
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p = 1000 kg/m^3 density of water
At nozzle: conservation of energy
h2 = 7 m
h1 = 2.6 m
g = 9.81 m/s^2
p v2^2/2 = pgh2
v2 = Sqr(2 * g * h2) m/s
From continuity of flow
In pipe
r1 = 0.04 / 2
a1 = pi * r1 ^ 2
At nozzle
r2 = 0.02 / 2
a2 = pi * r2 ^ 2
Assuming non-conservative forces are absent,
the volume/unit time is constant.
v1*a1 = v2*a2
v1 = v2 * a2 / a1 m/s
Now from Bernoulli, conservation of energy:
P2 = 101300 Pa …ATM.
u1 = u2
P1 + p v1^2/2 + p g h1 = P2 + p v2^2/2
Pump pressure:
P1 = P2 + (p * v2 ^ 2 / 2) – (p * v1 ^ 2 / 2) + (p * g * h1)
>>>>>P1 = 191184 Pa
Check:
u1 = 169970 J/m^3
u2 = 169970 J/m^3
Any problem, let me know.