Power of a Pump draining a flooded basement

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SUMMARY

The power delivered by the pump draining a flooded basement is calculated using the principles of fluid dynamics, specifically the Continuity and Bernoulli equations. The flow rate is determined to be 1.827 kg/s based on a hose radius of 1.01 cm and a velocity of 5.7 m/s. The calculated power output is approximately 52.99 Watts, although a discrepancy arises with another calculation yielding 54.07 Watts. The difference in results is attributed to significant figures used during calculations.

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  • Understanding of fluid dynamics principles, specifically Continuity and Bernoulli equations.
  • Ability to calculate cross-sectional area from radius measurements.
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  • Familiarity with significant figures in scientific calculations.
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Homework Statement



Water is pumped steadily out of a flooded basement at a speed of 5.7m/s, through a uniform hose of radius 1.01cm. The hose passes through a window 2.96m above the waterline. What is the power (in W) delivered by the pump?


Homework Equations



Continuity and Bernoulli principles

The Attempt at a Solution



By using the radius, the cross sectional area is found to be 3.2047 * 10^-4 m^2.
Multiply this by the velocity to find the flow rate I got: .001827 m^3/s or 1.827 kg/s.
Multiply this by gravity (9.8 m/s^2) and the height (2.96m), I got 52.99 Watts.

I don't know where I made a mistake, please help!
 
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Your method is right but I get 54.07 ( how many figures did you carry through the calcs?)
 
I tried 54.07 W but it's not correct either.
 

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