Chapter 1: Problem 20
A can of soft drink at room temperature is put into the refrigerator so that it will cool. Would you model the can of soft drink as a closed system or as an open system? Explain.
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Consider the flow of air through a wind turbine whose blades sweep an area of diameter \(D\) (in \(\mathrm{m}\) ). The average air velocity through the swept area is \(V\) (in \(\mathrm{m} / \mathrm{s}\) ). On the bases of the units of the quantities involved, show that the mass flow rate of air (in \(\mathrm{kg} / \mathrm{s}\) ) through the swept area is proportional to air density, the wind velocity, and the square of the diameter of the swept area.
Solve this system of three equations with three unknowns using EES: $$\begin{array}{c} x^{2} y-z=1 \\ x-3 y^{0.5}+x z=-2 \\ x+y-z=2 \end{array}$$
At sea level, the weight of 1 kg mass in SI units is 9.81 N. The weight of 1 lbm mass in English units is \((a) 1 \mathrm{lbf}\) \((b) 9.81 \mathrm{lbf}\) \((c) 32.2 \mathrm{lbf}\) \((d) 0.1 \mathrm{lbf}\) \((e) 0.031 \mathrm{lbf}\)
It is well-known that cold air feels much colder in windy weather than what the thermometer reading indicates because of the "chilling effect" of the wind. This effect is due to the increase in the convection heat transfer coefficient with increasing air velocities. The equivalent wind chill temperature in \(^{\circ} \mathrm{F}\) is given by \([\mathrm{ASHRAE},\) Handbook of Fundamentals (Atlanta, GA, \(1993 \text { ), p. } 8.15]\) $$\begin{aligned} T_{\mathrm{equiv}}=& 91.4-\left(91.4-T_{\text {anbient }}\right) \\ & \times(0.475-0.0203 V+0.304 \sqrt{V}) \end{aligned}$$ where \(V\) is the wind velocity in \(\mathrm{mi} / \mathrm{h}\) and \(T_{\text {ambicnt }}\) is the ambient air temperature in \(^{\circ} \mathrm{F}\) in calm air, which is taken to be air with light winds at speeds up to \(4 \mathrm{mi} / \mathrm{h}\). The constant \(91.4^{\circ} \mathrm{F}\) in the given equation is the mean skin temperature of a resting person in a comfortable environment. Windy air at temperature \(T_{\text {ambient }}\) and velocity \(V\) will feel as cold as the calm air at temperature \(T_{\text {equiv. }}\) Using proper conversion factors, obtain an equivalent relation in SI units where \(V\) is the wind velocity in \(\mathrm{km} / \mathrm{h}\) and \(T_{\text {ambient }}\) is the ambient air temperature in \(^{\circ} \mathrm{C}\)
The gas tank of a car is filled with a nozzle that discharges gasoline at a constant flow rate. Based on unit considerations of quantities, obtain a relation for the filling time in terms of the volume \(V\) of the \(\operatorname{tank}(\text { in } \mathrm{L})\) and the discharge rate of gasoline \(V(\text { in } \mathrm{L} / \mathrm{s})\)
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