A swimming team wants to know the force exerted by a swimmer\'s hands during fre

Question

A swimming team wants to know the force exerted by a swimmer's hands during freestyle swimming, so they can design an appropriate weight training program. You have been hired as a consultant. You set up an underwater camera and flow visualization system in the pool looking upwards as the swimmer passes over. The swimmer was told not to kick and to use only arm strokes. Using flow visualization software, you measure the flow pattern around the swimmer's hand at the time the swimmer's arm is vertical and pointing at the camera, which is shown in the Figure.

Calculate the force component (in Newton) that drives the swimmer forward, i.e., in the x direction, at the time the image was taken.

From the imaging software, you have measured:

u1 = u1A = u1B = 3.5 m s-1
d2A = 23 x 10-3 m
d1 = d1A = d1B = 20 x 10-3 m
d2B = 15 x 10-3 m

? = 25o

You can assume:

The effective area of the hand is a rectangle, 0.15 m x 0.25 m.

The density of the water is a constant, with ? = 1000 kg m-3.

The flow around the time the image was taken is approximately steady.

The pressure upstream where u1 was measured is the same on both sides of the hand, i.e. p1 = p1A = p1B.

The flow pattern is effectively two-dimensional, i.e., you would see the same pattern near the fingertips as near the wrist.

Explanation / Answer

force = ?*a*u cos?

where ? is density of water 1000 kg m-3.

a is effective area =0.15 m x 0.25 m.

angles substended is ?=25o

u =3.5 m s-1

so force exerted in x direction required for swiming is

= 1000x.15x.25x3.5x cos25o

=130.095 N

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