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!