What Is the Maximum Speed a Rower Can Achieve with 1 kW Power?

[marty456]

Homework Statement

Dear all, I need help with an old exam question. It goes as following:

The maximum power that a certain athlete can produce is equal to 1 kW. What is the theoretical maximum speed that a rower can obtain in a rowboat with a smooth exterior, a length of 4 meter and a 'wet' surface of 2.8 m^2.

Homework Equations

No equations are given and I can't think of any. However, the density of air (1.2 kg/m^3), the dynamic viscosity of air (1.8*10^-5 Pa s), the density of water (1000 kg/m^3), the dynamic viscosity of air (0.0010 Pa s) are all given, though it does not say which (if any) I should use.

The Attempt at a Solution

I have been attempting to recreate a formula based on the units of the various components. One formula for power = force * speed, so speed=Power/force. For force, which is in Newton, I tried multiplying the viscosity of the water with the 'wet' area. The resulting number would have Newton as its unit (Pa*s*m^2 is equal to kg*m/s=Newton). However, this left me with a speed in the 6 digits, which I don't think is a realistic answer for a row boat.
I have tried other combinations as well, but these don't result in the right unit (m/s). Please help.

 

[haruspex]

At sufficiently great speed, the main resistance comes from the inertia of the water. See https://en.wikipedia.org/wiki/Drag_(physics)#Drag_at_high_velocity. But to use that you'd need the x-sectional area.
If you're having to base it on viscosity of the water then I'm unsure how to proceed. In the ideal treatment you need to know the distance from the hull to effectively still water. See http://en.wikipedia.org/wiki/Viscosity#Shear_viscosity.
How did you calculate it?