Table II.

Details for Table 1: Time-averaged viscous dissipation rate, power loss, and analyses of assumptions 2,3, and 5

Model	1	2	3	4	5	6	7	8	9	10	AVG§	SD§§
Ėsim (mW)*1	0.56	1.87	2.68	3.88	3.69	5.97	4.16	3.56	0.87	11.7	3.89	3.19
Ėsim ∩ U⃑n(mW)*2	0.52	1.67	2.53	3.28	3.05	4.65	3.24	2.84	0.71	10.9	3.34	2.93
Ẇτ(μW)*3	1.47	3.34	2.11	1.67	1.33	5.95	4.07	3.04	2.08	3.7	2.88	1.45
Ẇq(μW)*4	−1.58	2.36	−1.09	2.29	1.72	10.03	1.16	22.9	0.39	11.6	4.98	7.68
Ėloss(mW)*5	0.52	1.67	2.53	3.28	3.05	4.65	3.24	2.82	0.71	10.9	3.33	2.92
Φ(mW)*6	0.52	1.64	2.42	3.17	2.93	4.56	3.14	2.76	0.7	10.4	3.22	2.79
ΔĖsim ǂ1	−7%	−12%	−6%	−18%	−21%	−28%	−28%	−26%	−22%	−8%	−17.7%	9.0%
Δ(Ėsim ∩ U⃑n) ǂ2	−8%	−12%	−6%	−19%	−21%	−28%	−28%	−25%	−23%	−8%	−17.7%	8.8%
ΔẆτ ǂ3	0.3%	0.2%	0.1%	0.1%	0.0%	0.1%	0.1%	0.1%	0.3%	0.0%	0.1%	0.1%
ΔẆq ǂ4	−0.3%	0.1%	0.0%	0.1%	0.1%	0.2%	0.0%	0.8%	0.1%	0.1%	0.1%	0.3%
ΔΦ ǂ5	0.6%	1.9%	4.5%	3.3%	3.9%	1.8%	3.2%	2.1%	1.6%	4.5%	2.7%	1.3%
§Avg = average value			§§SD = standard deviation
*1Ėsim			simplified power loss
*2Ėsim ∩ U⃑n			power loss with correctly calculated velocity profile (U⃑n)
*3Ẇτ = ∫CS τ⃑ · U⃑ dA			viscous work present on the control surface
*4 ${\dot{W}}_q=\frac{\partial }{\partial t}{\int }_V\rho \left(\frac{U^2}{2}\right)\mathit{\text{ dV}}$			effect of time-derivatives of dynamic pressure and volume
*5Ėloss = (Ėsim ∩ U⃑n) + Ẇτ − Ẇq			true power loss
*6Φ			viscous dissipation rate
ǂ1ΔĖsim = (Ėloss − Ėsim)/Ėloss			discrepancy between simplified and true power losses
ǂ2Δ(Ėsim ∩ U⃑n) = 1 ∸ Ėsim/(Ėsim ∩ U⃑n)			time-averaged percentage discrepancy between power loss obtained using an accurate spatial velocity profile (assumption #5) and true power loss.
ǂ3 ΔẆτ = Ẇτ/Ėloss			time-averaged effect of viscous work on the control surface, assumption #2
ǂ4 ΔẆq = Ẇq/Ėloss			time-averaged effect of control volume and dynamic pressure, assumption #3
ǂ5ΔΦ = (Ėloss − Φ)/Ėloss			time-averaged discrepancy between viscous dissipation rate and true power loss