Final answer:
To determine the minimum diameter of the pipe, use Bernoulli's equation and conservation of energy principles.
Step-by-step explanation:
To determine the minimum diameter of the pipe, we need to consider the Bernoulli's equation and the conservation of energy principles. According to Bernoulli's equation, the pressure difference between the large and small ends of the pipe will be equal to the difference in potential energy of the water at those two points.
Using the equation P1 - P2 = (1/2) * ρ * v^2 + ρ * g * h, where P1 is the pressure at the large end, P2 is the pressure at the small end, ρ is the density of water, v is the velocity of water at the small end, and h is the height difference between the two ends, we can solve for the gauge pressure.
To find the minimum diameter of the pipe, we can use the equation for the velocity of water at the small end: v = (2 * g * h)^0.5, where g is the acceleration due to gravity. By substituting this velocity into the Bernoulli's equation, we can solve for the gauge pressure.