Calculating Power of Pump in Flooded Basement

[duke_nemmerle]

Homework Statement

Water is pumped steadily out of a flooded basement at a speed of 5.0 m/s through a uniform hose of radius 1.0 cm. The hose passes out through a window 3.0m above the waterline. What is the power of the pump?

Homework Equations

The Attempt at a Solution

I actually correctly solved the problem by taking advantage of the fact that
$$P = \frac{\Delta W}{\Delta t }$$ which for us is $$P = \frac{\Delta m}{\Delta t} (gh + \frac{1}{2}v^{2})$$

My question is, if the force applied is constant, why can't I use $$P = \frac{F\Delta d}{\Delta t}$$ since it's a simple matter of finding the force and $$\frac{\Delta d}{\Delta t} = v$$ is given.

 

[luben]

hello duke, i think the force F you specify cannot be found without using Bernoulli equation.

 

[duke_nemmerle]

Yeah, I had actually found the force using an equation that is only good for static fluids, I'm going to see if using Bernoulli gets me the same result both ways. Thanks :)