Final answer:
The given statement that water is flowing at a velocity of 1.3 ft/sec in a 3-inch diameter pipe can not be said to be true or false because The Darcy-Weisbach equation requires additional information such as the length of the pipe (L) and the friction factor (f) to calculate the head loss.
Step-by-step explanation:
The student's question relates to the flow rate and diameter of the pipe in a fluid dynamics context, which is a topic in physics. Using the principles of continuity of flow for an incompressible fluid (such as water), we can relate flow rate and velocity to the cross-sectional area of the pipe.
To find the flow rate in liters per second (a), we use the equation:
Flow Rate (Q) = Velocity (v) × Cross-sectional Area (A)
First, we calculate the cross-sectional area, A = π × (d/2)^2, where d is the diameter of the pipe.
Then we multiply the area by the velocity to get the flow rate.
For part (b), to find the nozzle's inside diameter, we apply the equation of continuity, which states that the flow rate must be the same in both sections of the hose:
Q1 = Q2
A1 × v1 = A2 × v2
The area is related to the diameter, so by finding the second area using the velocity and the initial flow rate, we can find the second diameter.