(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

So the question i have involves finding the force exerted on a swimmer using only arm strokes through the water.

A snapshot of the swimmer is taken by a camera underwater when the swimmer's arm is vertical and pointing at the camera.

Here is a diagram of the hand:

(forgot to label the top stream as A and bottom stream as B)

The question asks to calculate the Force component that drives the swimmer forward (in this case the x direction), at the time the image was taken.

Given values are u_{1}=u_{1A}=u_{1B}= 3.5m/s

d_{1}=d_{1A}=d_{1B}= 20*10^-3 m

Angle [itex]\alpha[/itex] = 25 degrees

d_{2A}= 23*10^-3 m

d_{2B}= 15*10^-3 m

Given Assumptions

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

The density of water is 1000kg/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. P_{1}=P_{1A}=P_{1B}

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

2. Relevant equations

A_{1}V_{1}=A_{2}V_{2}

Bernoulli's Equation form of

1/2(V_{2}^2-V_{1}^2)=-1/ρ(P_{2}-P_{1})

3. The attempt at a solution

To start off with i found the velocities of each of the flow streams near the end (point 2)

To do this i used the ratios of the d's to get

V_{1}A_{1}=V_{2A}A_{2}(height will be the same so)

V_{1}d_{1}=V_{2A}d_{2A}

V_{2A}= d_{1}/d_{2A}* V_{1}

and i did the same for V_{2B}

So the values for the velocities i got were

V_{2A}=3.04 m/s

V_{2B}= 4.67 m/s

Using these values i put them into Bernoulli's Equation

(V_{2A}^2-V_{1}^2)=-1/ρ(P_{2A}-P_{1})

(V_{2B}^2-V_{1}^2)=-1/ρ(P_{2B}-P_{1})

sub values and get:

(P_{2A}-P_{1})= -1504.2 pascal

(P_{2B}-P_{1})= 4779.45 pascal

I then subbed for P_{1}and got

(P_{2A}-P_{2B})=-6283.65 pascal So this value is the Pressure difference between the flow streams.

I then used

(P_{2A}-P_{2B})*Area(hand) to get the force

=-235.63 N

then for the force in the x direction (since the force acts normal to the object)

-235.63*Cos(115degrees) = 99.58 N

The value sort of sounds reasonable but I'm not sure if I've made any errors going about this.

In particular is there anything in the y direction i need to include?

Any feedback on the working would be appreciated

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# Homework Help: Force exerted on a swimmer

Can you offer guidance or do you also need help?

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