A flat plate is 1.5m×1.5 m moves at 50 km per hour in stationary air of density 1.15kg/m31.15kg/m3. If the coefficient of drag and lift are 0.15 and 0.75 respectively, determine (i) The lift force (ii) The drag force (iii) The resultant force (iv) The power required to keep the plate in motion

 A flat plate is 1.5m$\times$1.5 m moves at 50 km per hour in stationary air of density 1.15kg/m3$1.15kg/m^3$. If the coefficient of drag and lift are 0.15 and 0.75 respectively, determine

(i) The lift force

(ii) The drag force

(iii) The resultant force

(iv) The power required to keep the plate in motion

Solution:- 

Given: -

Area of plate, A=1.5×1.5=2.25m2$A=1.5\times 1.5=2.25m^2$

Velocity of plate, V=50km/hr=50×100060×60=13.89m/s$V=50km/hr={\displaystyle \frac{50\times 1000}{60\times 60}}=13.89m/s$

Density of air, ρ=1.15kg/m3$\rho =1.15kg/m^3$

Coefficient of drag, CD=0.15$C_D=0.15$

Coefficient of lift, CL=0.75$C_L=0.75$

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(i) Lift Force, (FL$F_L$):-

FL=CLA×ρV22$F_L=C_{L}A\times {\displaystyle \frac{\rho V^2}{2}}$

FL=0.75×2.25×1.5×13.8922$F_L=0.75\times 2.25\times {\displaystyle \frac{1.5\times {13.89}^2}{2}}$

FL=187.20N$F_L=187.20N$

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(ii) Drag Force (FD$F_D$): -

FD=CDA×ρV22$F_D=C_{D}A\times {\displaystyle \frac{\rho V^2}{2}}$

FD=0.15×2.25×1.15×13.8922$F_D=0.15\times 2.25\times {\displaystyle \frac{1.15\times {13.89}^2}{2}}$

FD=37.44N$F_D=37.44N$

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(iii) Resultant Force, (FR$F_R$): -

FR=F2D+F2L−−−−−−−√$F_R=\sqrt{F_D^2+F_L^2}$

FR=37.442+187.202−−−−−−−−−−−−−√$F_R=\sqrt{{37.44}^2+{187.20}^2}$

FR=1400+35025−−−−−−−−−−−√$F_R=\sqrt{1400+35025}$

FR=190.85N$F_R=190.85N$

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(iv) Power required to keep the plate in motion: -

P=FD×V1000$P={\displaystyle \frac{F_D\times V}{1000}}$

P=37.425×13.891000$P={\displaystyle \frac{37.425\times 13.89}{1000}}$

P=0.519KW