question_answer 27)

A plane is in level flight at constant speed and each of its wings has an area of \[\frac{\vartriangle V}{V}=\left( 80\cdot 0\times 1\cdot 013\times {{10}^{5}} \right)\times 45\cdot 8\times {{10}^{-11}}\] If the speed of the air is 180 km/h over the lower wing and 234 km/h over the upper wing surface, determine the plane's mass. (Take air density to be \[1\,kg/{{m}^{3}}\]) \[g=9.8\,m/{{s}^{2}}\].

Answer:

Here, \[p'=\frac{1\cdot 30\times {{10}^{3}}}{1-3\cdot 712\times {{10}^{-3}}}=1\cdot 034\times {{10}^{3}}\text{kg }{{\text{m}}^{\text{-3}}}\]\[=37\times {{10}^{9}}\text{N }{{\text{m}}^{\text{2}}}\] \[atm=1\cdot 013\times {{10}^{5}}pa.\] \[\text{p=10 atm}=10\times 1\cdot 013\times {{10}^{5}}\] Upward force = \[pa;B=37\times {{10}^{\text{9}}}\text{N }{{\text{m}}^{\text{-2}}}\] As the plane is in level flight, so mg = \[=\frac{\vartriangle V}{V}=\frac{P}{B}=\frac{10\times 1\cdot 013\times {{10}^{5}}}{37\times {{10}^{9}}}\] Or \[=2\cdot 74\times {{10}^{-5}}\]\[\therefore \] \[\frac{\vartriangle V}{V}\]