To find the flow velocity of the fluid in the line, we need to use the equation for flow rate, which is given by
- flow rate = volume flow rate/area.
Since the flow meter is measuring the volume flow rate of the fluid in gallons per minute, and 1 gallon is equal to 231 cubic inches, the volume flow rate in cubic inches per minute is
- 18 gal/min * 231 in3/gal = 4178 in3/min.
To find the flow velocity, we need to divide this volume flow rate by the cross-sectional area of the line. The cross-sectional area of a circle is given by A = pi * r^2, where r is the radius of the circle. Since the diameter of the line is 1.0 inches, the radius is 1.0 inches / 2 = 0.5 inches. Plugging this value into the equation for the area gives us:
= pi * (0.5 inches)^2
= 0.785 inches^2
We can now use the equation for the flow rate to find the flow velocity:
- flow velocity = volume flow rate/area
= 4178 in3/min / 0.785 inches^2
= 5327 in/min
Rounding to the nearest whole number, we find that the flow velocity at the meter is 5327 inches per minute.