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

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SUMMARY

The discussion focuses on calculating the Volume Flow Rate of water leaving a faucet, given a gauge pressure of 102 kPa and a height of 10 m. The relevant equations include the Volume Flow Rate formula (Q = Av) and a simplified Bernoulli equation for velocity (v = √((Gauge Pressure - density of water * g * height) / (1/2 * density))). The user initially calculated a flow rate of 8 cm³/m but failed to convert the speed to the correct volume flow rate in cm³/s. The correct approach involves using the area of the faucet and the velocity derived from the Bernoulli equation.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically Bernoulli's equation.
  • Knowledge of Volume Flow Rate calculations (Q = Av).
  • Familiarity with unit conversions, particularly between cm³/m and cm³/s.
  • Basic physics concepts such as gauge pressure and density of water.
NEXT STEPS
  • Learn how to apply Bernoulli's equation in practical scenarios.
  • Study unit conversion techniques for fluid dynamics calculations.
  • Explore the effects of cross-sectional area on flow rates in pipes.
  • Investigate the relationship between pressure, height, and flow rate in fluid systems.
USEFUL FOR

Students in physics or engineering courses, particularly those studying fluid dynamics, as well as professionals involved in plumbing or hydraulic systems design.

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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