# Basic fluid mechanics question

1. Aug 26, 2007

### stinlin

1. The problem statement, all variables and given/known data

A sled slides along on the snow on a thin horizontal layer of water between the ice and the runners. The horizontal force that the water puts on the runners is equal to 1.2 lb when the sled's speed is 50 ft/s. The total area of both runners in contact with the water is 0.08 ft^2, and the viscosity of the water is 3.5(10^-5) lb*s/ft^2. Determine the thickness of the water layer under the runners. Assume a linear velocity distribution in the water layer.

2. Relevant equations

Shear stress = viscosity * (du/dy)

du/dy is the rate of strain.

3. The attempt at a solution

Well, because it has a linear velocity distribution, du/dy = Umax / h, where Umax is the maximum velocity and h is the height or depth of the fluid.

Umax = 50 ft/s
Max shear stress = P/A = 1.2 lb / 0.08 ft^2 = 15 lb/ft^2

So rearranging with substitutions, the equation looks like this:

h = (viscosity)*Umax/h

With numbers:

h = (3.5(10^-5) lb*s/ft^2) * 50 ft/s / 15 lb/ft^2 = 0.00175/15 ft

h = 11.7(10^-5) ft

That seems legit, no? But my book says 11.7(10^-4) ft. Now I know I shouldn't ALWAYS trust the book, but I just have a feeling I missed something if I'm off by only one order of magnitude. Thoughts?