Final answer:
The pressure that must be maintained just upstream of the nozzle to deliver the desired flow rate is equal to the atmospheric pressure.
Step-by-step explanation:
To determine the pressure that must be maintained just upstream of the nozzle to deliver the desired flow rate, we can use Bernoulli's equation. First, we need to calculate the velocity of the water at the nozzle. We can use the equation Q = A * v, where Q is the flow rate, A is the cross-sectional area, and v is the velocity.
Rearranging the equation to solve for v, we have v = Q / A. Substituting the given values of Q = 250 gal/min and A = π * (1.250/2)^2, we can find the velocity. Next, we use Bernoulli's equation, P1 + (1/2) * ρ * v1^2 = P2 + (1/2) * ρ * v2^2, where P1 and P2 are the pressures at the two respective points, ρ is the density of the fluid, and v1 and v2 are the velocities at those points.
Since the nozzle is attached to the hose, the velocities at both points will be the same, and the equation reduces to P1 = P2. Therefore, the pressure that must be maintained just upstream of the nozzle is the same as the pressure inside the nozzle, which is atmospheric pressure at sea level, approximately 14.7 psi or 101,325 Pa.