To solve this problem it is necessary to apply the equations given from Bernoulli's principle, which describes the behavior of a liquid moving along a streamline. Mathematically this expression can be given as,
[tex]P_1 + \frac{1}{2}\rho*v_1^2 + P_2 + \frac{1}{2}*\rho*v_2^2=0[/tex]
Where,
[tex]P_i =[/tex] Pressure at each state
[tex]\rho[/tex]= Density
[tex]v_i =[/tex] Velocity
Re-organizing the expression we can get that
[tex]P_1 - P_2 = \frac{1}{2}\rho (v_2^2 - v_1^2)[/tex]
Our values are given as
[tex]v_1 = 40m/s[/tex]
[tex]v_2 = 55m/s[/tex]
[tex]\rho_{water} = 1.2kg/m^3 \rightarrow[/tex] Normal Conditions
Replacing we have,
[tex]P_1 -P_2 = \frac{1}{2}*1.2*(55^2-40^2)[/tex]
[tex]P_1 - P_2 = 855Pa[/tex]
If we consider that there is a balance between the two states, the Force provided by gravity is equivalent to the Support Force, therefore
[tex]F_l = F_g[/tex]
Here the lift force is the product between the pressure difference previously found by the effective area of the aircraft, while the Force of gravity represents the weight. There,
[tex]F_g = W[/tex]
[tex]F_l = (P_2-P_1)A[/tex]
Equating,
[tex](P_1 - P_2)*A = W[/tex]
[tex]W = 855*17[/tex]
[tex]W = 14535 N[/tex]
Therefore the weight of the plane is 14535N
