Volume Flow Rate: Solve for Water Leaving Faucet in cm^3/s

AI Thread Summary
To determine the volume flow rate of water leaving the faucet, the gauge pressure of 102 kPa and the height of 10 m must be considered. The simplified Bernoulli equation is used to calculate the velocity of water, which is then multiplied by the cross-sectional area of the faucet (2.0 cm²) to find the volume flow rate. The initial attempt yielded an incorrect value of 8 cm³/m, indicating a misunderstanding in the conversion of velocity to volume flow rate. The correct approach involves ensuring that the velocity is in cm/s before applying it to the area for the final calculation. The solution requires careful attention to unit conversions and the application of the volume flow rate formula Q = Av.
kathmill
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Homework Statement


A pump at ground level creates a gauge pressure of 102 kPa in the water line supplying an apartment building. The water leaves the tank into a pipe at a negligible speed. It travels up 10 m through the building and exits through a faucet. The cross-sectional area of the faucet is 2.0 cm^2. What is the Volume Flow Rate of the water leaving the faucet in cm^3/s?


Homework Equations



Volume Flow Rate: Q=Av
Bernoulli equation simplified: v = square root of: (Gauge Pressure - density of water*g*height)/(1/2 density)

So put V into Q=Av and solve!?

The Attempt at a Solution



I found it to be: 8 cm^3/m

Where am I going wrong?
 
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You solved for the speed v (in m/s). You need the volume flow rate, which is Av.
 
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