Question

NEED HELP URGENT!! A small, horizontal pipe with cross-sectional area A is joined to a large horizontal pipe with cross-sectional area 2A.  Both pipes are at the same height, and completely filled with water (density 1000 kg/m^3).  What is the speed of the water in the large pipe if the speed in the small pipe is 1 m/s?

Answer 1

Refer to the diagram shown below.

v₁ = 1 m/s, the speed in the smaller pipe
ρ = 1000 kg/m³, the density of the water (constant)
A, m² = the cross-sectional area of the smaller pipe
2A, m² = the cross-sectional area of the larger pipe.

Let v₂ = the velocity of the water in the larger pipe.

The mass flow rate is constant, and it is

`Q = (\rho \, (kg)/(m^(3)) )*(v_(1) \, (m)/(s) )*(A \, m^(2)) = (\rho \, (kg)/(m^(3)) )*(v_(2) \, (m)/(s) )*(2A \, m^(2))`

Because v₁ = 1 m/s, obtain
ρ*v₂*(2A) = ρA
2v₂ = 1
v₂ = 1/2 m/s

Answer: 0.5 m/s