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A fully loaded boeing aircraft has a mass of 3.3xx10^(5)kg . Its total wing area is 500m^(2) .It is in level flight with a speed of 96.km//h. (a)Estimate the pressure difference between the lower and upper surfaces of the wings . (b) Estimate the fractional increase in thespeed of the air on the upper surface of the wing relative to the lower surface. (The density of air is rho=1.2kgm^(-3))(g=9.8ms^(-2)) |
| Answer» <html><body><p><<a href="https://interviewquestions.tuteehub.com/tag/p-588962" style="font-weight:bold;" target="_blank" title="Click to know more about P">P</a>></p>Solution :The weight of the boeing aircraft is balanced by the upward force <a href="https://interviewquestions.tuteehub.com/tag/due-433472" style="font-weight:bold;" target="_blank" title="Click to know more about DUE">DUE</a> to the pressure difference `=DeltaPxxA`<br/>`mg=DeltaPxxA`<br/>`thereforeDeltaP=(mg)/(A)`<br/>`=(3.3xx10^(<a href="https://interviewquestions.tuteehub.com/tag/5-319454" style="font-weight:bold;" target="_blank" title="Click to know more about 5">5</a>)xx9.8)/(500)`<br/>`0.06468xx10^(5)`<br/> `therefore` Pressure difference `=6468Nm^(-2)`<br/>(b)From Bernoulli.s equation,<br/>`P_(1)-P_(2)=(1)/(2)rho(v_(2)^(2)-v_(1)^(2))+rhog(h_(2)-h_(1))`<br/>Neglecting `h_(2)-h_(1)` for its small value,<br/>`thereforeP_(1)-P_(2)=(1)/(2)(rho(v_(2)^(2)-v_(1)^(2))`<br/>`therefore(2DeltaP)/(rho)=(v_(2)-v_(1))(v_(2)+v_(1))`<br/>`thereforev_(2)-v_(1)=(2DeltaP)/(rho(v_(2)+v_(1))=(DeltaP)/(rho((v_(2)+v_(1))/(2)))`...(1)<br/>Now average speed`ltvgt=(v_(1)+v_(2))/(2)`<br/>`=(960xx1000)/(<a href="https://interviewquestions.tuteehub.com/tag/3600-1859327" style="font-weight:bold;" target="_blank" title="Click to know more about 3600">3600</a>)`<br/>`=266.6ms^(-1)`<br/>`thereforev_(2)-v_(1)=(DeltaP)/(rholtvgt)=(6468)/(1.2xx266.6)`<br/> `=20.21ms^(-1)`<br/>`therefore(v_(2)-v_(1))/(ltvgt)=(20.21)/(267)"" (because` From equation (1))<br/> `=0.0756`<br/> `=0.8`<br/>Hence , speed above the wing needs to be only `8%` higher than that below.</body></html> | |