For the geometry shown in the sketch below, determine the layout of nodes and control volumes. Provide a scale drawing showing the problem geometry overlaid with the nodes and control volumes. Explain how to derive the energy balance equation for all the boundary control volumes.
GIVEN
Cylindrical geometry shown in the figure.
FIND
(a) A reasonable layout of nodes and control volumes
SKETCH
We do not know what the boundary conditions are so we cannot make any judgment about symmetry.
Therefore, we must assume that the problem is axisymmetric. Since Ro = 10 cm, let’s use ?r = 2.5 cm
giving 5 radial nodes. To accommodate the 45° cutout, let’s use a circumferential node spacing, ?o =
45°. The right side of the sketch shows the resulting layout of nodes and control volumes. Energy
balance equations for the control volumes at the circumferential boundary would be derived as
described. For those control volumes, we have conduction from three surrounding
control volumes and either convection, specified flux, or a specified temperature at the fourth surface,
depending on the boundary condition. For the control volumes along the two radial boundaries, we
have conduction from two surrounding control volumes. Treatment of the third surface would depend
on the boundary condition.
You might also like to view...
Using 1000 J of work, a toy elevator is raised from the ground floor to the second floor in 20 s. How much power does the elevator use?
A) 20 W B) 50 W C) 100 W D) 1000 W E) 20,000 W
Is it possible to see a virtual image?
A) No, since the rays that seem to emanate from a virtual image do not in fact emanate from the image. B) No, since virtual images do not really exist. C) Yes because the rays that appear to come from a virtual image can be focused by the eye just like those from an object. D) Yes, but only by using an additional lens to form a real image before the light reaches the eye.
A balloon of negligible mass is filled with 300 m3 of helium. How big a payload can the balloon lift? (The density of air is 1.29 kg/m3; the density of helium is 0.18 kg/m3.)
a. 150 kg c. 333 kg b. 300 kg d. 444 kg
Ellis and Randy are looking at a molecular absorption spectrum. The spectral lines appear to fall into two groups with a gap in the middle. Ellis says that this must be an absorption spectrum for transitions between the v = 0 and v = 1 vibrational states of a diatomic molecule. Randy says the gap in the middle must occur because a ?J = 0 transition is forbidden. Which one, if either, is correct,
and why? a. Ellis, because rotational levels are separated by greater energy differences than vibrational levels. b. Randy, because rotational levels are separated by greater energy differences than vibrational levels. c. Ellis, because the ?J = 0 transition is the most prominent spectral line in transitions between vibrational levels. d. Neither, because rotational levels are separated by greater energies that vibrational levels and ?J = 0 transitions are not forbidden. e. Both, because vibrational levels are separated by greater energy differences than rotational levels and ?J = 0 transitions are forbidden.