Need 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?

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


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

0.5 m/s

You get 6 for mechanical