How Is Lift Calculated Using the Bernoulli Principle for an Airplane Wing?

AI Thread Summary
Lift on an airplane wing can be calculated using the Bernoulli Principle by applying the equation P1 + (1/2)densityV1^2 = P2 + (1/2)densityV2^2. Given the air density of 1.29 kg/m^3 and speeds of 347 m/s over the top and 289 m/s under the wing, the pressure difference results in a value of 5.39 x 10^4 N/m^2. This pressure difference is then multiplied by the wing area of 84.5 m^2 to yield a lift force of approximately 4.6 x 10^6 N. The calculations confirm the application of Bernoulli's equation for determining lift. The method used for this calculation is deemed correct.
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Homework Statement



Find the lift in Newtons due to the Bernoulli Principle on a wing of a plane of area 84.5 m^2 if the air passes over the top and the bottom surfaces at speeds of 347m/s and 289 m/s


Homework Equations



P1+(1/2)densityV^2 =P2+(1/2)densityV^2

The Attempt at a Solution



Ok so i know the density of air is 1.29kg/m^3

so i plug into equation to get

1/2(1.29kg/m^3)(347m/s)^2= 1/2(1.29kg/m^3)(289m/s)^2

then i get answer of 5.39x10^4 N/m^2

then i use equation F=PA

and P is 5.39x10^4 N/m^2 and A is 84.5m^2

to get answer of 4.6x10^6 N

Am i correct ?
 
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By bernouili equation
Pa+1/2pva^2 = Pb =1/2pvb^2
1/2pvb^2-1/2pva^2 =Pa-Pb
deltaP = 1/2pvb^2-1/2pva^2
deltaP * A =Lift force
I think your method is correct
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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