A vessel contains 85 L of water at 10°C and atmospheric pressure. If the water is heated to 70°C, what will be the percentage change in its volume? What weight of water must be removed to maintain the volume at its original value? Use Appendix A.
Volume, \sout{V} _{10}=85 \mathrm{~L}=0.085 \mathrm{~m}^{3}
Table A.1 \gamma_{10}=9.804 \mathrm{kN} / \mathrm{m}^{3}, \quad \gamma_{70}=9.589 \mathrm{kN} / \mathrm{m}^{3}
Weight of water, W=\gamma \sout{V} =\gamma_{10} \sout{V} _{10}=\gamma_{70} \sout{V}_{70}
i.e., \quad 9.804(0.085) \mathrm{kN}=9.589 \sout{V} _{70} ; \quad \sout{V} _{70}=0.08691 \mathrm{~m}^{3}
\Delta \sout{V} =\sout{V} _{70}-\sout{V} _{10}=0.08691-0.08500=0.001906 \mathrm{~m}^{3} at \gamma_{70}
\Delta \sout{V}_{10}=0.001906 / 0.085=2.24 \% increase
Must remove (at \left.\gamma_{70}\right): \quad W\left(\frac{\Delta \sout{V} }{\sout{V} _{70}}\right)=\gamma_{70} \Delta \sout{V}
=\left(9589 \mathrm{~N} / \mathrm{m}^{3}\right)\left(0.001906 \mathrm{~m}^{3}\right)=18.27 \mathrm{~N} \quad
TABLE A.1 Physical properties of water at standard sea-level atmospheric pressure { }^a | ||||||||
Temperature, | Specific weight, | Density, | Absolute viscosity {}^b | Kinematic viscosity, {}^b | Surface tension, | Saturation vapor pressure, | Satur’n vapor pressure head, | Bulk modulus of elasticity, |
\boldsymbol{T} | \boldsymbol{\gamma} | \boldsymbol{\rho} | \boldsymbol{ \mu} | \boldsymbol{\nu} | \boldsymbol{\sigma} | \boldsymbol{ p_v} | \boldsymbol{ p_v}/ \boldsymbol{\gamma} | \boldsymbol{E_v} |
{ }^{\circ} \mathbf{F} | \mathbf{l b} / \mathbf{f t}^3 | \boldsymbol{ slugs/ft { }^3} | 10^{-6} \mathbf{lb} \cdot \mathrm{sec} / \mathbf{ft}^2 | 10^{-6} \mathbf{ft}^2 / \mathbf{sec} | \mathbf{lb} / \mathbf{ft} | psia | ft abs | psi |
32 { }^{\circ} \mathrm{F} | 62.42 | 1.940 | 37.46 | 19.31 | 0.00518 | 0.0885 | 0.204 | 293,000 |
40 { }^{\circ} \mathrm{F} | 62.43 | 1.940 | 32.29 | 16.64 | 0.00514 | 0.122 | 0.281 | 294,000 |
50 { }^{\circ} \mathrm{F} | 62.41 | 1.940 | 27.35 | 14.10 | 0.00509 | 0.178 | 0.411 | 305,000 |
60 { }^{\circ} \mathrm{F} | 62.37 | 1.938 | 23.59 | 12.17 | 0.00504 | 0.256 | 0.592 | 311,000 |
70 { }^{\circ} \mathrm{F} | 62.30 | 1.936 | 20.50 | 10.59 | 0.00498 | 0.363 | 0.839 | 320,000 |
80 { }^{\circ} \mathrm{F} | 62.22 | 1.934 | 17.99 | 9.30 | 0.00492 | 0.507 | 1.173 | 322,000 |
90 { }^{\circ} \mathrm{F} | 62.11 | 1.931 | 15.95 | 8.26 | 0.00486 | 0.698 | 1.618 | 323,000 |
100 { }^{\circ} \mathrm{F} | 62.00 | 1.927 | 14.24 | 7.39 | 0.00480 | 0.949 | 2.20 | 327,000 |
110 { }^{\circ} \mathrm{F} | 61.86 | 1.923 | 12.84 | 6.67 | 0.00473 | 1.275 | 2.97 | 331,000 |
120 { }^{\circ} \mathrm{F} | 61.71 | 1.918 | 11.68 | 6.09 | 0.00467 | 1.692 | 3.95 | 333,000 |
130 { }^{\circ} \mathrm{F} | 61.55 | 1.913 | 10.69 | 5.58 | 0.00460 | 2.22 | 5.19 | 334,000 |
140 { }^{\circ} \mathrm{F} | 61.38 | 1.908 | 9.81 | 5.14 | 0.00454 | 2.89 | 6.78 | 330,000 |
150 { }^{\circ} \mathrm{F} | 61.20 | 1.902 | 9.05 | 4.76 | 0.00447 | 3.72 | 8.75 | 328,000 |
160 { }^{\circ} \mathrm{F} | 61.00 | 1.896 | 8.38 | 4.42 | 0.00441 | 4.74 | 11.18 | 326,000 |
170 { }^{\circ} \mathrm{F} | 60.80 | 1.890 | 7.80 | 4.13 | 0.00434 | 5.99 | 14.19 | 322,000 |
180 { }^{\circ} \mathrm{F} | 60.58 | 1.883 | 7.26 | 3.85 | 0.00427 | 7.51 | 17.84 | 318,000 |
190 { }^{\circ} \mathrm{F} | 60.36 | 1.876 | 6.78 | 3.62 | 0.00420 | 9.34 | 22.28 | 313,000 |
200 { }^{\circ} \mathrm{F} | 60.12 | 1.868 | 6.37 | 3.41 | 0.00413 | 11.52 | 27.59 | 308,000 |
212 { }^{\circ} \mathrm{F} | 59.83 | 1.860 | 5.93 | 3.19 | 0.00404 | 14.69 | 35.36 | 300,000 |
{ }^{\circ} \mathbf{C} | \mathbf{kN} / \mathbf{m}^3 | \mathbf{~kg} / \mathbf{m}^3 | \mathbf{~N} \cdot \mathbf{s} / \mathbf{m}^2 | 10^{-6} \mathbf{~m}^2 / \mathbf{s} | \mathbf{N} / \mathbf{m} | \mathbf{kN} / \mathbf{m}^2 \text { abs } | \mathbf{m} \text { abs } | 10^6 \mathbf{kN} / \mathbf{m}^2 |
0 { }^{\circ} \mathrm{C} | 9.805 | 999.8 | 0.001781 | 1.785 | 0.0756 | 0.611 | 0.0623 | 2.02 |
5 { }^{\circ} \mathrm{C} | 9.807 | 1000.0 | 0.001518 | 1.519 | 0.0749 | 0.872 | 0.0889 | 2.06 |
10 { }^{\circ} \mathrm{C} | 9.804 | 999.7 | 0.001307 | 1.306 | 0.0742 | 1.230 | 0.1255 | 2.1 |
15 { }^{\circ} \mathrm{C} | 9.798 | 999.1 | 0.001139 | 1.139 | 0.0735 | 1.710 | 0.1745 | 2.14 |
20 { }^{\circ} \mathrm{C} | 9.789 | 998.2 | 0.001002 | 1.003 | 0.0728 | 2.34 | 0.239 | 2.18 |
25 { }^{\circ} \mathrm{C} | 9.777 | 997.0 | 0.000890 | 0.893 | 0.072 | 3.17 | 0.324 | 2.22 |
30 { }^{\circ} \mathrm{C} | 9.765 | 995.7 | 0.000798 | 0.800 | 0.0712 | 4.24 | 0.434 | 2.25 |
40 { }^{\circ} \mathrm{C} | 9.731 | 992.2 | 0.000653 | 0.658 | 0.0696 | 7.38 | 0.758 | 2.28 |
50 { }^{\circ} \mathrm{C} | 9.690 | 988.0 | 0.000547 | 0.553 | 0.0679 | 12.33 | 1.272 | 2.29 |
60 { }^{\circ} \mathrm{C} | 9.642 | 983.2 | 0.000466 | 0.474 | 0.0662 | 19.92 | 2.07 | 2.28 |
70 { }^{\circ} \mathrm{C} | 9.589 | 977.8 | 0.000404 | 0.413 | 0.0644 | 31.16 | 3.25 | 2.25 |
80 { }^{\circ} \mathrm{C} | 9.530 | 971.8 | 0.000354 | 0.364 | 0.0626 | 47.34 | 4.97 | 2.2 |
90 { }^{\circ} \mathrm{C} | 9.467 | 965.3 | 0.000315 | 0.326 | 0.0608 | 70.10 | 7.40 | 2.14 |
100 { }^{\circ} \mathrm{C} | 9.399 | 958.4 | 0.000282 | 0.294 | 0.0589 | 101.33 | 10.78 | 2.07 |
{ }^a In these tables, if (for example, at 32^{\circ} \mathrm{F} ) \mu is given as 37.46 and the units are 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2 then \mu=37.46 \times 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2. { }^b {\text {For viscosity, see also Figs. A.1 and A.2. }}. |