Question

The flow rate of corn syrup through a horizontal pipe of diameter 3 inches is 0.5 ft³/s. Find the velocity of this flow.

a) 1 ft/s
b) 2 ft/s
c) 3 ft/s
d) 4 ft/s

Answer 1

The velocity of the flow is approximately 10.18 ft/s.

Step-by-step explanation:

The flow rate of a fluid can be determined using the equation:

Flow Rate = Area × Velocity

In this problem, the flow rate is given as 0.5 ft³/s and the diameter of the pipe is given as 3 inches. To find the velocity, we need to calculate the area of the pipe using the formula:

Area = π × (radius)²

Since the diameter is given, we can find the radius by dividing the diameter by 2. So, the radius is 1.5 inches or 0.125 feet.

Plugging in the values:

Area = π × (0.125)² = 0.049087 ft²

Now, we can rearrange the flow rate equation to solve for velocity:

Velocity = Flow Rate / Area = 0.5 ft³/s / 0.049087 ft² = 10.18 ft/s

Therefore, the velocity of this flow is approximately 10.18 ft/s.