### Mechanical Properties Of Fluids Question 4

#### Question 4 - 29 January - Shift 2

A fully loaded boeing aircraft has a mass of $5.4 \times 10^{5} kg$. Its total wing area is $500 m^{2}$. It is in level flight with a speed of $1080 km / h$. If the density of air $\rho$ is $1.2 kg m^{-3}$, the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be $(g=10 m / s^{2})$

(1) 16

(2) 6

(3) 8

(4) 10

## Show Answer

#### Answer: (4)

#### Solution:

#### Formula: Bernoulli’s Theorem

$P_2 A-P_1 A=5.4 \times 10^{5} \times g$

$P_2-P_1=\frac{5.4 \times 10^{6}}{500}=5.4 \times 2 \times 10^{2} \times 10$

$ =10.8 \times 10^{3} $

$P_2+0+\frac{1}{2} \rho V_2{ }^{2}=P_1+0+\frac{1}{2} \rho V_1{ }^{2}$

$P_2-P_1=\frac{1}{2} \rho(V_1^{2}-V_2^{2})=\frac{1}{2} \rho(V_1-V_2)(V_1+V_2)$

$10.8 \times 10^{3}=\frac{1}{2} \times 1.2(V_1-V_2) \times 2 \times 3 \times 10^{2}$

$10.8 \times 10=3.6(V_1-V_2)$

$V_1-V_2=30$

$(\frac{V_1-V_2}{V}) \times 100=\frac{30}{300} \times 100=10 \%$