Water flows through a horizontal pipe (from a wider area to narrow area section) and then out into the atmosphere at a speed v1 15 m/s. The diameters of the wide and narrow sections of the pipe are 5.0 cm and 3.0 cm.
What volume of water flows into the atmosphere during a 10 min period?
Question
Answer:
V = 6.36 m³
Explanation:
For this exercise we will use fluid mechanics relations, starting with the continuity equation.
Let’s write the flow equation
Q = v₁ A₁
The area of a circle is
A = π r²
Radius is half the diameter
A = π/4 d²
Q = v₁ π/4 d₁²
Q = π/ 4 15 0.03 2
Q = 0.0106 m3 / s
The volume of water in t = 10 min = 10 60 = 600 s
Q = V / t
V = Q t
V = 0.0106 600
V = 6.36 m³