http://www.denialville.com/flow-rate-faucet/
Faucet Physic problem?
I need help on C. I can' seem to figur it out
A long horizontal hose of diameter 4.8 cm is connected to a faucet. At the other end, there is a nozzle of diameter 1.2 cm. Water squirts from the nozzle at velocity 26 m/sec. Assume that the water has no viscosity or other form of energy dissipation.
a) What is the velocity of the water in the hose ?
m/s *
1.625 OK
HELP: Flow rate must be constant, because volume is conserved for incompressible fluid.
b) What is the pressure differential between the water in the hose and water in the nozzle ?
Pa
337 NO
HELP: Use Bernoulli's Law.
c) How long will it take to fill a tub of volume 130 liters with the hose ?
sec
HELP: Remember the definition of the flow rate.
A1 v1 = A2 v2
d1^2 v1 = d2^2 v2
v2 = [d1/d2]^2 v1 = (1/4)^2 *26 = 1.625m/s
-------------------------------------------------------
P + 1/2 ρ v^2 = K.
[p2 -p1] =1/2 ρ [v1^2 - v2^2] = 1/2* 1000 [26^2 - 1.625^2]
[p2 -p1] = 336680 Pa.
----------------------------------------------------------------------
Power = force x velocity
and velocity = flow rate /area.
Therefore
Power = force x flow rate /area.
Since force / area is pressure
Power = pressure x flow rate
In the problem pressure = h ρ g = 120* 1000* 9.81
Power = 120* 1000* 9.81* 710 = 835812 K.W.= 835.8 M W.
----------------------------------------------------------------------
Flow rate = A v= π [d^2 / 4 ] * v
= π [0.012 ^2 / 4 ] * 26 = 0.00294 m^3 /s
= π [0.048 ^2 / 4 ] * 1.625 = 0.00294 m^3 /s
130 liters = 0.13 m^3
t = 0.13/ 0.00294 = 44.2 s
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