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 2 years ago
Introduction to Mechanics1. Units and Dimensional AnalysisLearning ActivitiesChallenge Problems
Problem 3: Dimensional Analysis Solution
The speed of a sailboat or any other craft that does not plane is limited by the wave it makes – it can’t climb uphill over the front of the wave. What is the maximum speed you’d expect?
Hint: relevant quantities might be the length l of the boat, the density ! of the water, and the gravitational acceleration g: Vboatl^Xp^Yg^Z
How to understand
The maximum speed of a singlehull displacement boat in SI units is given by
Vboat
= (1.25 m ^(1/2)s^(1))*l^0.5
where l length of the hull at the waterline is measured in meters. So our estimation based
on dimensional analysis requires a coefficient
v = 0.40 ( lg)^(1/2)
Thanks!!!
 2 years ago
Introduction to Mechanics1. Units and Dimensional AnalysisLearning ActivitiesChallenge Problems Problem 3: Dimensional Analysis Solution The speed of a sailboat or any other craft that does not plane is limited by the wave it makes – it can’t climb uphill over the front of the wave. What is the maximum speed you’d expect? Hint: relevant quantities might be the length l of the boat, the density ! of the water, and the gravitational acceleration g: Vboatl^Xp^Yg^Z How to understand The maximum speed of a singlehull displacement boat in SI units is given by Vboat = (1.25 m ^(1/2)s^(1))*l^0.5 where l length of the hull at the waterline is measured in meters. So our estimation based on dimensional analysis requires a coefficient v = 0.40 ( lg)^(1/2) Thanks!!!

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