-->

Mechanical Properties Of Fluids

Question
CBSEENPH11020004

In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are 70 m s–1and 63 m s–1 respectively. What is the lift on the wing if its area is 2.5 m2? Take the density of air to be 1.3 kg m–3.

Solution
Speed of wind on the upper surface of the wing, V1 = 70 m/s
Speed of wind on the lower surface of the wing, V2 = 63 m/s
Area of the wing, A = 2.5 m2

Density of air, ρ = 1.3 kg m–3
According to Bernoulli's Theorem, 

straight P subscript 1 space plus space 1 half ρV subscript 1 squared space equals space straight P subscript 2 space space plus space 1 half ρV subscript 2 squared space
space space space space space space space space space space straight P subscript 2 space space minus straight P subscript 1 space equals space 1 half straight rho space left parenthesis straight V subscript 1 squared space minus space straight V subscript 2 squared right parenthesis

where comma space

straight P subscript 1 space equals space Pressure space on space the space upper space surface space of space the space wing

straight P subscript 2 space equals space Pressure space on space the space lower space surface space of space the space wing 
Pressure space difference space between space the space upper space and
lower space of space the space wing space provides space lift space to space the space aeroplane. space

Lift space on space the space wing space equals space left parenthesis straight P subscript 2 space minus straight P subscript 1 right parenthesis space straight A space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space bevelled 1 half space straight rho space space left parenthesis straight V subscript 1 squared space minus space straight V subscript 2 squared right parenthesis space straight A space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space bevelled 1 half space cross times 1.3 cross times left square bracket space 70 squared space minus space 63 squared space right square bracket space cross times space 2.5 space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1512.87 space straight N space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 1.51 space cross times space 10 to the power of 3 space end exponent straight N

Therefore comma space the space lift space on space the space wing space of space the space aeroplane space
is space 1.51 space cross times space 10 cubed space straight N.