**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**

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**29, 30, 34, 35, 42,
43**

29: P_{a }= rgh
where r
= density of water and P_{a} = 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 = P_{atmospheric}
A

42 and 43: Realize
that P_{input} must = P_{output}. Since Pressure = Force/Area, that means that Force_{input}/Area_{input}
must equal Force_{output}/Area_{output}. Substitute Force/Area wherever you see
pressure. Hope that helps!

**9.3 Buoyancy and Archimedes Principle**

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**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?**

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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 = F_{b}
= rgV. Make sure all of your units match up!

63: r of
real gold is 1.93 x 10^{4} kg/m^{3}.

**9.4 Fluid Dynamics
and Bernoullli’s Equation**

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

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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 v_{xdirection
}doesn’t change during flight.

77: Q = A_{1}v_{1}
where you solve for v_{1}.
Then, from the equation of continuity, A_{1}v_{1} = A_{2}v_{2}. Use the new A_{2} to solve for v_{2}. Finally, use Bernoulli’s principle. Realize that y_{1}=y_{2}.

Answers:

30: a) 1.5 x 10^{5} Pa b)
2.5 x 10^{5} Pa.

34: 2.1 x 10^{3}
Pa

42: a) 7.5 x 10^{6}
Pa b) 1.5 x 10^{4} N

46: c

54: 2.6 x 10^{3}
kg

56: 2.0 x 10^{3}
kg/m^{3}

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 m^{3}/s b)
1.6 m/s

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