A distribution system for liquid propane is made from steel hydraulic tube, 32 mm OD × 2.0 mm wall. Several 90° bends are required to fit the tubes to the other equipment in the system. The specifications call for the radius to the inside of each bend to be 200 mm. When the system carries 160

Question

A distribution system for liquid propane is made from steel hydraulic tube, [latex] 32 mm OD × 2.0 mm[/latex] wall. Several 90° bends are required to fit the tubes to the other equipment in the system. The specifications call for the radius to the inside of each bend to be 200 mm. When the system carries 160 L/min of propane at 25°C, compute the energy loss due to each bend.

Accepted Answer

Darcy’s equation should be used to compute the energy loss with the [latex] L_e/D[/latex] ratio for the bends found from Fig. 10.28. First, let’s determine r/D, recalling that D is the inside diameter of the tube and r is the radius to the centerline of the tube. From Appendix G.2 we find D = 28.0 mm = 0.028 m. The radius r must be computed from

[latex] r = R_i + D_o/2 [/latex]

where [latex] D_o = 32.0mm[/latex], the outside diameter of the tube, as found from Appendix G.2. Completion of the calculation gives

[latex] r = 200mm + \left(32.0mm ight)/2 = 216mm [/latex]

and

r/D = 216 mm/28.0 mm = 7.71

From Fig. 10.28 we find the equivalent-length ratio to be 23.
We must now compute the velocity to complete the evaluation of the energy loss from Darcy’s equation:

[latex] v = \frac{Q}{A} = \frac{160L/min}{6.158 imes 10^{-4} m^2}\frac{1.0m^3/s}{60000L/min}=4.33m/s [/latex]

The relative roughness is

[latex] D/\epsilon = \left(0.028m ight) \left(1.5 imes 10^{-6}m ight) =18667[/latex]

Then, we can find [latex] f_T = 0.0108 [/latex] from the Moody diagram (Fig. 8.7) in the zone of complete turbulence.

Then,

[latex] K = f_T \left(\frac{L_e}{D} ight) = 0.0108\left(23 ight) =0.248[/latex]

Now the energy loss can be computed:

[latex] h_L = K\frac{v^2}{2g} = 0.248\frac{\left(4.33 ight)^2 }{\left(2 ight)\left(9.81 ight) } = 0.237m = 0.237N·m/N[/latex]

Question 10.10: A distribution system for liquid propane is made from steel ...

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