The Speedy Water Adventure
Question:
Imagine a world where water flows through a square pipe with a side length of 2 in a hydraulic system at a rate of 15 gallons/second. What is the velocity of the adventurous water in inches per second?
Answer:
The velocity of the water flowing through the square pipe is 866.25 inches/second.
Explanation:
To calculate the velocity of water flowing through the square pipe, we can use the equation:
Velocity = Flow rate / Cross-sectional area
Step 1: Calculate the cross-sectional area of the square pipe.
The cross-sectional area of a square can be found by multiplying the length of one side by itself. In this case, the side length of the square pipe is 2 units.
Cross-sectional area = 2 units * 2 units = 4 square units
Step 2: Convert the flow rate from gallons/second to cubic inches/second.
Given that there are 231 cubic inches in a gallon, we can convert the flow rate as follows:
Flow rate in cubic inches/second = Flow rate in gallons/second * 231 cubic inches/gallon
Flow rate in cubic inches/second = 15 gallons/second * 231 cubic inches/gallon = 3465 cubic inches/second
Step 3: Calculate the velocity of water.
Now, we can use the formula mentioned earlier to calculate the velocity:
Velocity = Flow rate / Cross-sectional area
Velocity = 3465 cubic inches/second / 4 square units = 866.25 inches/second
Therefore, the velocity of water flowing through the square pipe in this adventurous hydraulic system is 866.25 inches/second. What a speedy adventure it is!