Question

Increasing this To this Increases the capacity

pipe diameter diameter by a factor of
(inches) (inches)
4 6 2.25
4 8 4.00
6 8 1.78
6 10 2.78
6 12 4.00
8 10 1.56
8 12 2.25
8 15 3.52
10 12 1.44
10 15 2.25
12 15 1.56

A 12 inch pipeline is flowing full of water and is necked down to a four inch pipeline, does the velocity of the water in the 4 inch line increase or decrease and by a factor of ________________?
a. Increases, 9 fold
b. Decreases it 9 fold
c. Flow is not impacted

Answer 1

Option A). When a 12 inch pipeline is necked down to a four inch pipeline, the velocity of the water in the 4 inch line increases by a factor of 9.

Step-by-step explanation:

The water velocity in the 4-inch line rises when a 12-inch pipeline is necked down to a 4-inch pipeline. The Venturi effect states that as the diameter of a constriction decreases, the speed of an incompressible fluid through it increases. According to the Venturi effect, the fluid's speed is inversely related to the diameter squared. Thus, the water's velocity will increase by a factor of 9 (3 squared) if the diameter reduces by a factor of 3 (from 12 inches to 4 inches).