Answer:
D₂ = 2.738 cm
Explanation:
Continuity equation
The continuity equation is nothing more than a particular case of the principle of conservation of mass. It is based on the flow rate (Q) of the fluid must remain constant throughout the entire pipeline.
Since the flow rate is the product of the surface of a section of the duct because of the speed with which the fluid flows, we will have to comply with two points of the same pipeline:
Q = v*A : Flow Equation
where:
Q = Flow in (m³/s)
A is the surface of the cross sections of points 1 and 2 of the duct.
v is the flow velocity at points 1 and 2 of the pipe.
It can be concluded that since the flow rate must be kept constant throughout the entire duct, when the section decreases, the flow rate increases in the same proportion and vice versa.
Data
D₁= 6.0 cm : faucet diameter
v₁ = 5 m/s : speed of fluid in the faucet
v₂ = 20 m/s : speed of fluid in the nozzle
Area calculation
A = (π*D²)/4
A₁ = (π*D₁²)/4
A₂ = (π*D₂²)/4
Continuity equation
Q₁ = Q₂
v₁A₁ = v₂A₂
v₁(π*D₁²)/4 = v₂(π*D₂²)/4 : We divide by (π/4) both sides of the equation
v₁ (D₁)² = v₂(D₂)²
We replace data
6 *(5)² = 20*(D₂)²
150 = 20*(D₂)²
(150 /20) = (D₂)²
7.5 = (D₂)²
[tex]D_{2} = \sqrt{7.5}[/tex]
D₂ = 2.738 cm : nozzle diameter
