First slide

Fluid dynamics

Question

Speeds of air blow on the upper and lower surfaces of a wing of an aeroplane are $V_{1} a n d V_{2}$ respectively. If A be the cross sectional area of the wing and $ρ$ be the density of air, then the upward lift is

Easy

A

$\frac{1}{2} ρ A (V_{1} - V_{2})$
B

$\frac{1}{4} ρ A (V_{1}^{2} - V_{2}^{2})$
C

$\frac{1}{2} ρ A (V_{1}^{2} - V_{2}^{2})$
D

$\frac{1}{4} ρ A (V_{1}^{2} + V_{2}^{2})$

Solution

(3)

Applying Bernoulli's equation between points (1) and (2),
$\begin{array}{l} P_{1} + \frac{1}{2} ρ V_{1}^{2} = P_{2} + \frac{1}{2} ρ V_{2}^{2} \\ \Rightarrow P_{2} - P_{1} = \frac{1}{2} P (V_{1}^{2} - V_{2}^{2}) \\ ∴ U p w a r d l i f t = (P_{2} - P_{1}) A = \frac{1}{2} ρ A (V_{1}^{2} - V_{2}^{2}) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App