Answer:
The net resultant force is 23.64 kN with an angle of 12.9° with positive x-axis.
Explanation:
The mass flow rate of the fluid at inlet is equal to:
Where
p = density = 1000 kg/m³
d₁ = inlet diameter = 30 cm = 0.3 m
V₁ = velocity of fluid = 5 m/s
This mass flow is constant through the duct, thus:
minlet = moulet
Where
d₂ = outlet diameter = 15 cm = 0.15 m
V₂ = ?
Clearing V₂:
Bernoulli's equation will be used to calculate the pressure at the outlet:
Where:
P₁ = pressure at inlet = 300x10³ Pa
P₂ = pressure at exit = ?
z₁ and z₂ = datum heads = z₁ = 0.5 m z₂ = 0
The force in x-direction using the moment expression is equal to:
Where
β = momentum flux = 1.04
The force in y-direction using the moment expression is:
The net resultant force is equal to:
The angle of resultant force is equal to:
θ = tan⁻¹(Fy/Fx) = tan⁻¹(-5.28/-23.04) = 12.9° with positive x-axis.