(a) What is the pressure difference between the lower and upper surfaces of the

Question

(a) What is the pressure difference between the lower and upper surfaces of the wings?
Pa

(b) If the speed of air under the wings is 231 m/s, what is the speed of the air over the wings? Assume air has a density of 1.29 kg/m3.
m/s

(c) Explain why all aircraft have a "ceiling," a maximum operational altitude.

The density of air  ---Select--- increases decreases with increasing height, resulting in a  ---Select--- smaller greater pressure difference. Beyond the maximum operational altitude, the pressure difference can no longer support the aircraft.

Explanation / Answer

In this simplified example, the net force due to pressure on the wing must counter the weight of the plane. The weight of the plane is W=m*g. = F Now, pressure is force spread over an area, so P=F/A. In our case, the force must be equal to the weight of the plane, so P=W/A

b) P = mg /A = 8.60*10^4 *9.81 / 95 =8880.63158 Pa answer

We will start with Bernoulli's equation: p1 + 1/2*rho*v1^2 = p2 + 1/2*rho*v2^2 for points 1 and 2 along the same path in steady, incompressible flow.

We assume that the air on top and bottom of the wing starts upstream at the same conditions. That leads us to pt + 1/2*rho*vt^2 = pb + 1/2*rho*vb^2 (t=top, b=bottom).
Rearrange: 1/2*rho*vt^2 - 1/2*rho*vb^2 = pb - pt. Here, (pb - pt) is   the pressure difference

1/2*rho*vt^2 - 1/2*rho*vb^2 = pb - pt = 8880.63158

0.5 * 1.29 * vt^2 - 0.5* 1.29* 231^2 = 8880.63158

solve for vt we got

vt = 259.093 m/s answer

(c) As you can see, density plays a very significant role in the lift equations. If density is too low (high altitude) the airplane may not be able to get enough of a pressure difference to offset its weight

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.