- #1
mbrmbrg
- 496
- 2
Homework Statement
Water is pumped steadily out of a flooded basement at a speed of 5.5 m/s through a uniform hose of radius 1.2 cm. The hose passes out through a window 2.9 m above the waterline. What is the power of the pump?
Homework Equations
[tex]R_v=Av[/tex]
[tex]R_m=\rho Av[/tex]
where P is power, W is work, and K is kinetic engery:
[tex]P=\frac{W}{\Delta t}[/tex]
[tex]W=\Delta K=\frac{1}{2}mv^2-\frac{1}{2}mv_0^2[/tex]
The Attempt at a Solution
[tex]R_v=Av=\pi r^2v=(\pi)(.012 m)^2(5.5 m/s)=0.002488 m^3/s[/tex]
[tex]R_m=\rho Av=(1000 kg/m^3)(0.002488m^3/s)=2.488kg/s[/tex]
[tex]Power=\frac{W}{\Delta t}=\frac{\Delta K}{\Delta t}=(\frac{1}{2}m{v_f}^2-\frac{1}{2}m{v_i}^2)/(\Delta t)[/tex]
Take delta time to be 1s, initial velocity (water sitting in basement) to be 0m/s, final velocity (water in pipe) to be 5.5m/s, mass dealt with in one second is 2.488kg.
NOTE: I think my error lies here; something was assigned a totally evil value. Probably my choices of velocity.
But going with the values I picked, I got [tex]P=(\frac{1}{2})(2.488 kg/s)(5.5 m/s)^2=37.63W[/tex]
This be wrong. I be sad.