Question

PLEASE HELP!!! 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 pressure of the water in the large pipe if the speed of the water in the small pipe is one m/s and the pressure of the water in the small pipe is 1000 Pa?

Answer 1

Let point 1 be the small pipe and 2 be the larger pipe. Using the continuity equation,

ρ₁A₁v₁ = ρ₂A₂v₂

Since density is the same,
A₁v₁ = A₂v₂
A(1) = (2A)(v₂)
v₂ = 0.5 m/s

Then, we use the mechanical energy balance:

(P₂ - P₁)/ρ + (v₂² - v₁²)/2 = 0
(P₂ - 1000 Pa)/ 1000 kg/m³ + (0.5² - 1²)/2 = 0
P₂ = 1375 Pa

Thus, the pressure of the larger pipe is 1,375 Pa.