Calculating Mass Flow Rate: Pump Water Through Nozzle

[Colts]

Homework Statement

A pump steadily delivers water through a hose terminated
by a nozzle. The exit of the nozzle has a diameter of 0.6 cm
and is located 10 m above the pump inlet pipe, which has a
diameter of 1.2 cm. The pressure is equal to 1 bar at both the
inlet and the exit, and the temperature is constant at 20° C. The
magnitude of the power input required by the pump is 1.5 kW,
and the acceleration of gravity is g = 9.81 m/s^2. Determine
the mass flow rate delivered by the pump, in kg/s.

Homework Equations

Not sure. I think
m_dot (deltaPE) = W

I don't know if I can use the work by the pump though.
m_dot = rho*Volumetric flow rate

The Attempt at a Solution

Well these are the only equations I can think of and I'm not sure if these are right. Any help where to go form here would be appreciated.

 

[rude man]

Someone else pitch in! I get an unwieldy third-order polynomial!