Question

1. An air-plane has an effective wing surface area of 12.0 m² that is generating the lift force. In level flight the air speed over the top of the wings is 58.5 m/s, while the air speed beneath the wings is 45.5 m/s. What is the weight of the plane?(The density of air is 1.29 kg/m³) (in N)

2. Water at a pressure of 3.60 atm at street level flows into an office building at a speed of 0.50 m/s through a pipe 5.00 cm in diameter. The pipes taper down to 2.40 cm in diameter by the top floor, 22.0 m above. Calculate the water pressure in such a pipe on the top floor. (in Pa)

Answer 1

1.

using bernoulli's theorem

P1 + 0.5rho*V1^2 = P2 + 0.5*rho*V2^2

P2 - P1 = 0.5*rho*(V1^2 - V2^2)

Net Upward force on plane wing will be

Force = Pressure difference*Area

F = (P2 - P1)*A

F = 0.5*rho*(V1^2 - V2^2)*A

rho = air density = 1.29 kg/m^3

A = effective surface area of wings = 12.0 m^2

V1 = Speed of air above the wings = 58.5 m/sec

V2 = Speed of air below the wings = 45.5 m/sec

F = 0.5*1.29*(58.5^2 - 45.5^2)*12.0

F = 10464.48 N

F = Net upward force of air on the plane = 1.05*10^4 N

Now Using Force balance in vertical direction:

Net Upward Force = Weight of plane = 1.05*10^4 N