Sometimes we understand the effect of a certain error, but we do not take the time to determine its magnitude. Such can be the case of making an error with regard to pipe schedule. Assume that a six-inch ultrasonic flowmeter in liquid service is designed and calibrated for Schedule 40 pipe, but is instead installed on a Schedule 80 pipe. How much does the flow measurement change due to the measurement of a different velocity in the metering section?

A. Flow measurement increases by approximately 10%
B. Flow measurement increases by approximately 5%
C. No effect
D. Flow measurement decreases by approximately 5%
E. Flow measurement decreases by approximately 10%

Commentary
The inside diameter of six-inch Schedule 40 and Schedule 80 pipes are 6.065 and 5.761 inches respectively. Because the inside diameter of the Schedule 80 pipe is smaller, the same amount of liquid will travel at a higher velocity in the Schedule 80 pipe metering section than in the Schedule 40 pipe. Therefore, when the flowmeter measures the fluid velocity in the metering section, the flowmeter measurement in the Schedule 80 metering section will be higher. This effectively eliminates Answer C, Answer D, and Answer E. The issue then becomes quantifying how much higher the flowmeter will measure.

Applying the equation of continuity, it can be seen that the ratio of the velocity in the Schedule 80 metering section to the velocity in the Schedule 40 metering section is proportional to the area of the metering
sections.

Q = A1 * v1 = A2 * v2

Q = A Schedule 40 * v Schedule 40 = A Schedule 80 * v Schedule 80
(v Schedule 80 / v Schedule 40) = (A Schedule 40 / A Schedule 80)

The area of the pipe is proportional to the square of the diameter,
A = 1⁄4 (pie) D2

so the ratio of the velocities is:
(v Schedule 80 / v Schedule 40) = (D2 Schedule 40 * / D2 Schedule 80 )
= (6.0652 / 5.7612)
= 1.108

Therefore, the velocity increases by almost 11 percent, so the best answer is Answer A.