Question

An ideal wind-turbine, 12 m in diameter, operates at a theoretical efficiency ($$\eta_{th}$$) (equation given below) of 50% in $$u_2$$ = 14 m/s wind. If the air density is 1.2 kg/$$m^3$$ and $$\eta_{th} = \frac{(u_1 + u_4)(u_1^2 - u_4^2)}{2u_1^3}$$ $$u_2 = u_3 = (u_1 + u_4) / 2$$ $$P_1 = P_4 = P_{atm}$$ Determine, a) The axial force on the windmill. (assume uniform flow at positions) b) The mean (gage) pressures immediately in front of ($$P_2 - P_{atm}$$) and behind ($$P_3 - P_{atm}$$) the disc, c) The shaft power developed by the turbine.

Name: an ideal wind turbine 12 m in diameter operates at a theoretical efficiency etath equation given below of 50 in u2 14 ms wind if the air density is 12 kgm3 and etath fracu1 u4u12 u422 71808
Uploaded: 2023-11-30T19:10:28-08:00
Duration: 1 min 33 s
Channel: Kratika Bhadauria
Description: an ideal wind turbine 12 m in diameter operates at a theoretical efficiency etath equation given below of 50 in u2 14 ms wind if the air density is 12 kgm3 and etath fracu1 u4u12 u422 71808

          An ideal wind-turbine, 12 m in diameter, operates at a theoretical efficiency ($$\eta_{th}$$) (equation given below) of 50% in $$u_2$$ = 14 m/s wind. If the air density is 1.2 kg/$$m^3$$ and

$$\eta_{th} = \frac{(u_1 + u_4)(u_1^2 - u_4^2)}{2u_1^3}$$

$$u_2 = u_3 = (u_1 + u_4) / 2$$

$$P_1 = P_4 = P_{atm}$$

Determine,

a) The axial force on the windmill. (assume uniform flow at positions)

b) The mean (gage) pressures immediately in front of ($$P_2 - P_{atm}$$) and behind ($$P_3 - P_{atm}$$) the disc,

c) The shaft power developed by the turbine.

$an ideal wind turbine 12 m in diameter operates at a theoretical efficiency etath equation given below of 50 in u2 14 ms wind if the air density is 12 kgm3 and etath fracu1 u4u12 u422 71808$

Added by Brian A.

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