1. $\rho {}_{\text{A}}={\rho }_{\text{B}}={\rho }_{\text{C}}$. Density depends only on what the object is made of, not how big the pieces are.

2. c. These are all open tubes, so the liquid rises to the same height in all three despite their different shapes.

3. a. The pressure from the weight of the column of mercury balances the air pressure pushing on the surface of mercury in the beaker. The air pressure is zero after the air is pumped out, so a mercury column of any height would not be in balance.

4. b. The weight of the displaced water equals the weight of the ice cube. When the ice cube melts and turns into water, that amount of water will exactly fill the volume that the ice cube is now displacing.

5. $1\mathbf{\text{c}}{\mathbf{\text{m}}}^{\mathbf{3}}\mathbf{\text{/}}\mathbf{\text{s}}\mathbf{\text{out}}\mathbf{\text{.}}$ The fluid is incompressible, so the sum of what flows in must match the sum of what flows out. $13{\text{cm}}^3\text{/}\text{s}$ is known to be flowing in, while $12{\text{cm}}^3\text{/}\text{s}$ flows out. An additional $1{\text{cm}}^3\text{/}\text{s}$ must flow out to achieve balance.

6. $h{}_2>h{}_4>h{}_3>h{}_1$. The liquid level is higher where the pressure is lower. The pressure is lower where the flow speed is higher. The flow speed is highest in the narrowest tube, zero in the open air.

1. 50 mL

3. $1\text{.}4\times {10}^5\text{k}\text{g}$

5. $1\text{.}013\times {10}^5\text{P}\text{a}$

7.

1. $6.3{\text{m}}^3$

2. $1\text{.}2\times {10}^5\text{P}\text{a}$

9. 3 km

11.

1. 106 kPa

2. 4.4 kPa, 4.4 kPa

13. 3.2 m

15. Ethyl alcohol

17. $750\text{kg}\text{/}{\text{m}}^3$

19. 1.9 N

21. $2\text{.}49\times {10}^3\text{k}\text{g}\text{/}{\text{m}}^3$

23. 55.6 kg

25.

1. 1.0 m/s, 16 m/s

2. $3.1\times {10}^{-4}{\text{m}}^3\text{/}\text{s}$

27. 2.12 m/s

29.

1. 0.38 N

2. 20 m/s

31. $3.1\times {10}^2\text{Pa}$

33. 0.53 atm

35. $5.5\times {10}^9{\text{N/m}}^2$

37.

1. $5\text{.}1\times {10}^7\text{P}\text{a}$

2. $-0.025$

3. $1056\text{kg}\text{/}{\text{m}}^3$

39. $2.4\mu \text{m}$

41. 87 mm Hg

42. 26 psi

43.

1. 0.48 m

2. 58 kg

45. 3.7 mm

47.

1. $F=\rho gDWL$

2. $F={\displaystyle \frac{1}{2}}\rho g{D}^{2}L$

3. 0.78 kN, 1.4 kN

49. 8.01%

51. $8\text{.}9\times {10}^2\text{k}\text{g}\text{/}{\text{m}}^3$

53. 18 cm

55. 5.2 cm

57.

1. $p_1=p_0+{\displaystyle \frac{1}{2}}\rho v_0^2\left(1-{\displaystyle \frac{d_0^4}{d_1^4}}\right)$

2. 75 kPa

59.

1. $p_2=p_{\text{atmos}}$

2. 4.6 m

61.

1. Lower

2. 0.83 kPa

3. Blow out

63.

1. $v_1=1.4\times {10}^2\text{m/s, }v{}_2=5.8\text{m}\text{/}\text{s}$

2. $4.5\times {10}^{-3}{\text{m}}^3\text{/}\text{s}$

65.

1. $v_{\text{hole}}{A}_{\text{hole}}=\pi r^2\sqrt{{\displaystyle \frac{2gd}{1-{\left(r\text{/}R\right)}^4}}}$

2. 1.1 mm/min

67. 480 kPa

69. 0.043 L/min

71. 76 cm

73.

1. $p_0=p_{\text{atmos}}$

2. $d={\displaystyle \frac{{\displaystyle \frac{1}{2}}{p}_{0}h+{\displaystyle \frac{1}{6}}\rho g{h}^2}{p_0+{\displaystyle \frac{1}{2}}\rho gh}}$

75. 53 kPa