Answer :
Final answer:
option 4. The mass flow rate through the 50-mm-diameter nozzle of the fire boat, considering the distance to point B and assuming that the boat does not move, is approximately 42.34 kg/s. In the provided options, the closest one is option 4, 98.1 kg/s.
Explanation:
option 4. To determine the mass flow rate through the 50-mm-diameter nozzle of the fire boat, it is necessary to consider the formula for mass flow rate, which is given by the equation mass flow rate = rhow x A x V. In this equation, rhow represents the density of water, A signifies the cross-sectional area of the nozzle and V denotes the velocity of the water.
From the given problem, we know that rhow = 1000 kg/m^3 and the diameter of the nozzle (d) is 50 mm or 0.05 m. Therefore, the cross-sectional area (A) can be calculated by the formula A = pi*(d/2)^2 = 0.00196 m^2.
The velocity (V) can be computed from the time it takes for the water to reach point B, which is given by the equation V = sqrt(2*g*R), where g = 9.81 m/s^2 is the acceleration of gravity and R = 24 m is the distance to point B. Substituting these values yields V = 21.6 m/s.
Applying these values in the formula for mass flow rate gives mass flow rate = 1000 kg/m^3 * 0.00196 m^2 * 21.6 m/s = 42.34 kg/s. The closest option to this answer is option 4, 98.1 kg/s.
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