Final answer:
The Reynolds number for flow in the fire hose and nozzle indicates turbulent flow, as it is greater than 2000. It is calculated based on the flow rate, fluid density, velocity, and radius of the hose or pipe. Given the provided data about flow rates and diameters, the flow in both the fire hose and nozzle must be turbulent.
Step-by-step explanation:
The Reynolds number (NR) is a dimensionless quantity used in fluid mechanics to characterize the flow of fluids. It determines whether the flow is turbulent or laminar. According to the given information, for flow through a fire hose and nozzle to be considered turbulent, the Reynolds number must be greater than 3000. For laminar flow, the Reynolds number should be below about 2000. Based on provided data, calculating the Reynolds number for flow in a fire hose with an inside diameter of 6.40 cm and a nozzle with a diameter of 3.00 cm, and a flow rate of 40.0 L/s showed that the Reynolds number is greater than 2000. Thus, the flow in both the fire hose and the nozzle is turbulent, not laminar.
To solidify the understanding, it is essential to know that the Reynolds number is calculated using the formula NR = 2pvr where p is the density of the fluid, v is the mean velocity of the fluid, and r is the radius of the pipe. In this context, the values for the flow in the nozzle indicated significantly high Reynolds numbers, well above 2000, which rules out laminar flow in the garden hose and nozzle with the given flow rate of 0.500 L/s. Therefore, the answer to the question is (a) greater than 2000, which signifies turbulent flow.