Answer to Question #278936 in Classical Mechanics for joseph

Question

6-36. Reconsider the helicopter in Prob. 6-35, except that it is hovering on top of a 2200-m-high mountain where the air density is 0.987 kg/m3. Noting that the unloaded helicopter blades must rotate at 550 rpm to hover at sea level, determine the blade rotational velocity to hover at the higher altitude. Also determine the percent increase in the required power input to hover at 2200 m altitude relative to that at sea level. Answers. 601 rpm, 9.3 percent

6-38 Water flowing in a horizontal 25-cm-diameter pipe at 8 m/s and 300 kPa gage enters a 90° bend reducing section, which connects to a 15-cm-diameter vertical pipe. The inlet of the bend is 50 cm above the exit. Neglecting any frictional and gravitational effects, determine the net resultant force exerted on the reducer by the water. Take the momentum-flux correction factor to be 1.04.

Answer 1

$\dot m=\rho A_1v_1=393~\frac{kg}s,$

$A_1v_1=A_2v_2,$ $v_2=22.2~\frac ms,$

$\frac{p_1}{\rho g}+\frac{v_1^2}{2g}+z_1=\frac{p_2}{\rho g}+\frac{v_2^2}{2g}+z_2,$

$p_2=90.5~kPa,$

$F_x=-\beta\dot mv_1-p_1A_1=-18~kN,$

$F_y=-\beta\dot mv_2-p_2A_2=-3.8~kN,$

$F=\sqrt{F_x^2+F_y^2}=18.4~kN,$

$\theta=\arctan\frac{F_y}{F_x}=11.9°$ with positive x-axis.