Holooly Plus Logo

Question 2.SP.4: A vessel contains 85 L of water at 10°C and atmospheric pres......

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.

2.4
Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

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. }}.

 

A1_917590
A2_917590

Related Answered Questions

Question: 2.SP.10

Verified Answer:

Table A.1 at 10^{\circ} \mathrm{C}: \quad \...
Question: 2.SP.11

Verified Answer:

From Appendix A, Table A.3, the pressure of the st...