Answer:
12 m/s
Explanation:
Using the continuity equation, which is an extension of the conservation of mass law
ρ₁A₁v₁ = ρ₂A₂v₂
where 1 and 2 indicate the conditions at two different points of flow, in this case, point 1 is any normal position in the pip and point 2 is the conditions at the restriction.
ρ = density of the fluid flowing; note that the density of the fluid flowing (water) is constant all through the fluid's flow
A₁ = Cross sectional Area of the pipe at point 1 = (πD₁²/4)
A₂ = Cross sectional Area of the pipe at the restriction = (πD₂²/4)
v₁ = velocity of the fluid flowing at point 1 = 3 m/s
v₂ = velocity of the fluid flowing at The restriction = ?
ρ₁A₁v₁ = ρ₂A₂v₂
Becomes
A₁v₁ = A₂v₂ (since ρ₁ = ρ₂)
(πD₁²/4) × 3 = (πD₂²/4) × v₂
3D₁² = D₂² × v₂
But
D₂ = (D₁/2)
And D₂² = (D₁²/4)
3D₁² = D₂² × v₂
3D₁² = (D₁²/4) × v₂
(D₁²/4) × v₂ = 3D₁²
v₂ = 4×3 = 12 m/s
