Answer :

Final answer:

The question references pressure testing of a 1" orange brush hose but provides a scenario for solving fluid dynamics problems, specifically finding the water pressure supplied by a faucet, evaluating its reasonability, and calculating the Reynolds number for the given flow rate through a garden hose. So the correct option is C.

Explanation:

To address a student's question regarding the pressure to which a 1" orange brush hose is tested, one needs to account for various factors such as the manufacturer's specifications and industry standards. However, based on the question prompt, we need to deal with a specific hypothetical situation relating to the flow of water through a garden hose which is a different matter. To solve this problem, we must first utilize the continuity equation and Bernoulli's principle to find the water pressure.

(a) By applying the equation of continuity A1V1 = A2V2 and Bernoulli's equation for a horizontal flow which indicates that P1 + 0.5ρV1² = P2 + 0.5ρV2² where ρ is the density of water and V is the velocity of fluid at points 1 and 2, we can solve for the water pressure supplied by the faucet. First, we need to determine the velocity of the water exiting the hose, which we can do by converting the flow rate from liters per second to cubic meters per second and then dividing by the cross-sectional area of the hose:

(b) Once we have calculated the pressure supplied by the faucet, we must assess its reasonability. High pressure could indicate a risk of hose or fixture damage, and in real-world scenarios, it is important to adhere to specific safety standards.

(c) Discussing the reasonability of the premise involves questioning whether the hypothetical scenario provides realistic conditions, such as the flow rate of 50.0 L/s, which might be exceedingly high for a typical garden hose's diameter and could not be achieved without exceedingly high pressure, which leads us to examine the hose specifications in relation to their typical use and limitations.

(d) The Reynolds number can be calculated using the formula Re = ρVD/η, where D is the diameter of the pipe and η is the dynamic viscosity of the fluid. A high Reynolds number would suggest turbulent flow which could be important for understanding the flow characteristics within the hose.

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Rewritten by : Barada