Question 2.SP.10: Water at 10°C stands in a clean glass tube of 2−mm diameter ......

Water at 10°C stands in a clean glass tube of 2−mm diameter at a height of 35 mm . What is the true static height?

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Table A.1 at $10^{\circ} \mathrm{C}: \quad \gamma=9804 \mathrm{~N} / \mathrm{m}^{3}, \sigma=0.0742 \mathrm{~N} / \mathrm{m}$.

Sec. $2.12$ for clean glass tube: $\quad \theta=0^{\circ}$

Eq. (2.12): $\quad h=\frac{2 \sigma}{\gamma r}=\frac{2(0.0742 \mathrm{~N} / \mathrm{m})}{\left(9804 \mathrm{~N} / \mathrm{m}^{3}\right) 0.001 \mathrm{~m}}$

$=0.01514 \mathrm{~m}=15.14 \mathrm{~mm}$

Sec. 2.12: True static height $=35.00-15.14=19.86 \mathrm{~mm}$

$h=\frac{2 \sigma \cos \theta}{\gamma r}$          (2.12)

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

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