The drag on a body moving in a fluid depends on the properties of the fluid, the size and...

The drag on a body moving in a fluid depends on the properties of the fluid, the size and the shape of the body, and probably most importantly, the velocity of the body. We find that for high velocities, the fluid density is important but the “stickiness” (or viscosity) of the fluid is not. The frontal area of the object is important. You might expect that there will be more drag on a double-decker bus moving at 60 miles per hour than on a sports car moving at 60 miles per hour.

The table below gives some data for tests of several spheres placed in air and in water. The terminal velocity, the point at which the velocity becomes constant when the weight is balanced by the drag, is shown.

(a) Plot the drag on the ordinate and the velocity of the object on the abscissa for each fluid on a separate plot. Use the graphs to answer the following question: What is the drag on a baseball in gasoline (specific gravity = 0.72) at a speed of 30 feet per second? You may struggle with this, but do the best you can.

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(b) Now complete a dimensional analysis of this situation and replot the data. First, recognize that the important parameters are the ball diameter (use the silhouette area of a circle), the density of the fluid, the drag, and the velocity. You will find a single dimensionless ratio that combines these parameters.

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(c) Compute the value of this ratio for the eight tests. Be sure in your analysis that you use consistent units so that the final ratio is truly unitless.

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(d) Use this result to help you answer question (a) again.