Here is one of my homework questions from fluid mechanics. It involves an ice skater and ice. See if you can find the answer for the question. The solution is shown; all you have to do is plug in the values. Post a comment with your answer and I will let you know if you got it right.
A female freestyle ice skater, weighting 100 lbf, glides on one skate at speed V = 20 ft/s. Her weight is supported by a thin film of liquid water melted from the ice by the pressure of the skate blade. Assume the blade is L = 11.5 in. long and w = 0.125 in. wide, and that the water film is h = 0.0000575 in. thick. Estimate the deceleration of the skater that results from viscous shear in the water film, if end effects are neglected.
Find Deceleration
Velocity v=20 ft/s
Weight w=100 lbf
Blade length L=11.5/12 ft
Blade thickness t=0.125/12 ft
Water film thickness h=0.0000575/12 ft
μ at 32°F is μ=3.68*〖10〗^5 (lbf*ft)/s^2
Solution
F=ma
m=w/g
τ= μ du/dy
F=τA
A=L*t
τ= μ du/dy= μ u/y= μ v/h
F=τA=ma
τA=ma
a=τA/m
a=[(μ*v/h)(L*t)]/(w/g)
