A.  Fluid Mechanics Homework

50 points



Note:  For this homework, Capital letter V is volume and lower case v is velocity.


9.2 Pressure and Pascal’s Principle


29, 30, 34, 35, 42, 43


29:  Pa = rgh where r = density of water and Pa = atmospheric pressure.  Be sure that all units match up before doing calculation.)

34:  P = F/A and recall that the force is going to be the normal force – and of course the normal force is a component vector of the force mg.

35:  Calculate the surface area of the can.  F = Patmospheric A

42 and 43:  Realize that Pinput must = Poutput.  Since Pressure = Force/Area, that means that Forceinput/Areainput must equal Forceoutput/Areaoutput.  Substitute Force/Area wherever you see pressure.  Hope that helps!



9.3  Buoyancy and Archimedes Principle


46, 47, 49, 51, 54, 55, 56, 63  Also, answer this question:  Assume you are in a boat on a lake and you have a bowling ball in your boat.  If you drop the ball into the water (ease it in, no splashing), what happens to the water level of the lake?  Does it go up, go down or stay the same?


49:  Try it!  Think about it.  If it did change the volume in some way, what do you think that would do to the law of conservation of mass?

54:  weight = Fb = rgV.   Make sure all of your units match up!

63:  r of real gold is 1.93 x 104 kg/m3.


9.4 Fluid Dynamics and Bernoullli’s Equation


64-69, 70, 71, 74, 75, 77


74:  Q = Av = V/t

75:  a)  v =  - our old friend.        b)  These are all horizontal projectiles.  So, first figure out time of fall (which is completely due to the height) and then use that time to find displacement in the x direction.  Recall that vxdirection doesn’t change during flight.

77:  Q = A1v1 where you solve for v1.  Then, from the equation of continuity, A1v1 = A2v2.  Use the new A2 to solve for v2.  Finally, use Bernoulli’s principle.  Realize that y1=y2.



30:  a)  1.5 x 105 Pa    b)  2.5 x 105 Pa.

34:  2.1 x 103 Pa

42:  a) 7.5 x 106 Pa    b)  1.5 x 104 N

46:  c

54:  2.6 x 103 kg

56:  2.0 x 103 kg/m3

64:  Figure it out for yourself.  We’ll discuss in class.

66:  c

68:  Figure it out for yourself.  We’ll discuss in class.

70:  0.98 m/s

74:  a)  0.11 m3/s      b)  1.6 m/s