Question 4.SP.1: Air at 100° F and under a pressure of 40 psia flows in a 1......
Air at 100° F and under a pressure of 40 psia flows in a 10-in-diameter ventilation duct at a mean velocity of 30 fps a. Find the mass flow rate.
Step-by-Step
Table A.5 for air: \quad R=1715 \mathrm{ft} \cdot 1 \mathrm{~b} /\left(\mathrm{slug} \cdot{ }^{\circ} \mathrm{R}\right)
From Eq. (2.4): \quad \rho=\frac{p}{R T}=\frac{40(144)}{1715(460+100)}=0.00600 \mathrm{slug} / \mathrm{ft}^{3}
Eq. (4.4): \quad \dot{m}=\rho A V=(0.00600) \frac{\pi}{4}\left(\frac{10}{12}\right)^{2}(30)=0.0981 \mathrm{slug} / \mathrm{sec} \quad
\frac{p}{\rho}=p v=R T (2.4)
\dot{m}=\rho \int_A u d A=\rho A V=\rho Q (4.4)
| TABLE A.5 Physical properties of common gases at standard sea-level atmospheric pressure { }^a . | ||||||||
| Gas | Chemical formula | Molar mass , \mathbf{ M} | Density \rho , | Absolute viscosity, {}^ b | Gas constant, \boldsymbol{R} | Specific heat, c_p \quad c_v | Specific heat ratio, k=c_p / c_v | |
| \textbf { at } 68^{\circ} \mathbf{F} | – | slug/ slug-mol | \textbf { slug/ft }{ }^3 | 10^{-6} \mathbf{lb} \cdot \mathbf{sec}^2 \mathbf{ft}^2 | \begin{aligned}& \mathbf{f t} \cdot \mathbf{l b} /\left(\text { slug } \cdot{ }^{\circ} \mathbf{R}\right) \\& =\mathbf{f t}^2 /\left(\sec ^2 \cdot{ }^{\circ} \mathbf{R}\right)\end{aligned} | \begin{aligned}& \mathbf{f t} \cdot \mathbf{l b} /\left(\text { slug } \cdot{ }^{\circ} \mathbf{R}\right) \\& =\mathbf{f t}^2 /\left(\sec ^2 \cdot{ }^{\circ} \mathbf{R}\right)\end{aligned} | – | |
| Air carbon | 28.96 | 0.00231 | 0.376 | 1,715 | 6,000 | 4,285 | 1.40 | |
| dioxide carbon | CO_2 | 44.01 | 0.00354 | 0.310 | 1,123 | 5,132 | 4,009 | 1.28 |
| quad monoxide | CO | 28.01 | 0.00226 | 0.380 | 1,778 | 6,218 | 4,440 | 1.40 |
| Helium | He | 4.003 | 0.000323 | 0.411 | 12,420 | 31,230 | 18,810 | 1.66 |
| Hydrogen | H_2 | 2.016 | 0.000162 | 0.189 | 24,680 | 86,390 | 61,710 | 1.40 |
| Methane | CH_4 | 16.04 | 0.00129 | 0.280 | 3,100 | 13,400 | 10,300 | 1.30 |
| Nitrogen | N_2 | 28.02 | 0.00226 | 0.368 | 1,773 | 6,210 | 4,437 | 1.40 |
| Oxygen | O_2 | 32.00 | 0.00258 | 0.418 | 1,554 | 5,437 | 3,883 | 1.40 |
| Water vapor | H_2O | 18.02 | 0.00145 | 0.212 | 2,760 | 11,110 | 8,350 | 1.33 |
| \textbf { at } 20^{\circ} \mathbf{C} | – | kg / kg-mol | \mathbf{kg} / \mathbf{m}^3 | 10^{-6} \mathbf{~N} \cdot \mathbf{s} / \mathbf{m}^2 | \begin{aligned}& \mathbf{N} \cdot \mathbf{m} /(\mathbf{kg} \cdot \mathbf{K}) \\& =\mathbf{m}^2 /\left(\mathbf{s}^2 \cdot \mathbf{K}\right)\end{aligned} | \begin{aligned} & \mathbf{N} \cdot \mathbf{m} /(\mathbf{k g} \cdot \mathbf{K}) \\ & =\mathbf{m}^2 /\left(\mathbf{s}^2 \cdot \mathbf{K}\right) \end{aligned} | – | |
| Air carbon | 28.96 | 1.205 | 18.0 | 287 | 1003 | 716 | 1.40 | |
| dioxide carbon | CO_2 | 44.01 | 1.84 | 14.8 | 188 | 858 | 670 | 1.28 |
| quad monoxide | CO | 28.01 | 1.16 | 18.2 | 297 | 1040 | 743 | 1.40 |
| Helium | He | 4.003 | 0.166 | 19.7 | 2077 | 5220 | 3143 | 1.66 |
| Hydrogen | H_2 | 2.016 | 0.0839 | 9.0 | 4120 | 14450 | 10330 | 1.40 |
| Methane | CH_4 | 16.04 | 0.668 | 13.4 | 520 | 2250 | 1730 | 1.30 |
| Nitrogen | N_2 | 28.02 | 1.16 | 17.6 | 297 | 1040 | 743 | 1.40 |
| Oxygen | O_2 | 32.00 | 1.33 | 20.0 | 260 | 909 | 649 | 1.40 |
| Water vapor | H_2O | 18.02 | 0.747 | 10.1 | 462 | 1862 | 1400 | 1.33 |
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