Final answer:
Without additional information such as the water velocity at the nozzle and assumptions made in the calculation, we cannot accurately provide the force required to hold a fire hose nozzle based on the given hose and nozzle diameters and the flow rate. The formula that would typically be used is F = ρAv^2, but cannot be applied without this missing information. So, the best answer is e, none of them.
Step-by-step explanation:
The student is asking about the force required to hold a fire hose nozzle based on the flow rate of water and the difference in diameter between the hose and the nozzle.
To solve this, you can apply the principles of the conservation of momentum along with the cross-sectional areas of the hose and nozzle and the velocity of the water.
Since the question does not provide information regarding the initial velocity or gauge pressure, simplifications and assumptions would need to be made, specifically assuming negligible resistance and hence a straight application of Bernoulli's theorem may not yield the force directly without further data.
However, without additional data or clarification on the conditions such as the water speed at the nozzle and other factors like the effect of air resistance and gravity, we cannot provide a detailed step-by-step solution to accurately calculate the force needed to hold the nozzle.
If we had the water velocity at the nozzle, we could apply the formula F = ρAv^2 (where F is force, ρ is the density of the water, A is the cross-sectional area of the nozzle, and v is the velocity of water at the nozzle) to find the force required to hold the nozzle.
So, the best answer is e, none of them.
Q: Provided the diameter of the fire hose is 7 cm, and the water running through the hose flows at 420 L/min, how much force does she need to hold the nozzle if its diameter is 0.75 cm?
A. 196 N
B. 168 N
C. 35 N
D. 2.94 N
E) none of them