Question 23.5: A mixing tank, like the one shown in Fig. 23-18, is being fi...
A mixing tank, like the one shown in Fig. 23-18, is being filled with solution. An ultrasonic sensor is located at the top of the tank. The tank is 10 feet in diameter and 15 feet tall. The mixing process in the tank requires 1021 \ ft^3 of solution. Solve for the required height of solution needed in the tank and the round-trip time the ultrasonic waves will have at this particular height. Assume the tank and solution are both at room temperature. The tank can be modeled as a cylinder.
Volume of a cylinder: V = πr^2 h
Where r is the radius in feet and h is the height in feet
This formula can be rewritten solving for height of the cylinder when the volume is known:
V = πr^2 h
h=\frac{V}{\pi r^2}
h=\frac{1021 \ ft^3}{π(5 ft)^2}
h = 12.999 ft
The ultrasonic waves travel at 1126 feet per second through air at room temperature. The time required to travel 2.001 feet (15 feet – 12.999 feet) to the surface of the solution and then back to the sensor is calculated as shown here:
t_{Round-trip}=\frac{Distance \ to \ object}{Speed \ of \ ultrasonic \ waves} =time of one-way trip × 2
t_{Round-trip}\frac{2.001 \ ft}{1126 \frac{ft}{sec} }= 1.777 \ ms × 2
t_{Round-trip}= 3.554 ms