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

Fluid Mechanics With Engineering Applications [917590]

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.

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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 $\mu=37.46 \times 10^{-6} \mathrm{lb} \cdot \mathrm{sec} / \mathrm{ft}^2$ . ${ }^b {\text {For viscosity, see also Figs. A.1 and A.2. }}$ .