PSS2 Fluids

Piston Problem: The piston shown in cross section in the figure (right) is filled with oil. (The “cylinder” is the large portion at the bottom right, and the areas above letter A and below letter B are circular.) Find the total force exerted by the fluid on the end of the cylinder at A and at B.

PSS2 Fluids

Hint: In a balloon, the pressure is usually not much higher than outside the balloon.

The tank in the figure is filled with water (depth d). At the bottom of one of the sidewalls there is a hatch with height h and width w. (a) determine the magnitude of the force the water exerts on the hatch assuming d>h. (b, extra challenge) find the magnitude of the torque exerted by the water on the hinges. (b) Extra integration practice: repeat (a) for d<h

Draw a) a velocity map and b) a streamline visualization for water flowing (in) through an 8 inch diameter pipe which gradually narrows to a 2 inch diameter pipe (out). Be sure both diagrams show easily at a glance which regions have relatively higher/lower velocity. If you can, give values for the ratios of Φin/Φout and vin/vout; if you can’t give a value for either ratio, say what else you would need to know to determine the ratio. How much flux would you need at the input to be sure the speed of the water coming out had a speed of at least 1.5 m/s?