Final answer:
The precise type of foam proportioner is not identified, but pressure changes in a hose are explained using Bernoulli's principle, where pressure is influenced by elevation and hose diameter changes.
Step-by-step explanation:
The type of foam proportioner that is directly attached to the pump panel outlet or connected at some point in the hose lay is not specified in the provided context. However, the context given describes a scenario dealing with the principles of fluid mechanics, particularly Bernoulli's principle. To solve for pressure at different points in a hose, we apply Bernoulli's equation which relates pressure, velocity, and height.
(a) When the hose has a 3.00-cm inside diameter and rises 2.50 m above the pump, the pressure at this point can be calculated if we know the initial pressure and velocity of the fluid. Since these details are not provided, we cannot calculate the exact pressure. However, we know that as the hose rises, the pressure will decrease due to the increase in gravitational potential energy.
(b) When the hose goes over the foundation wall, drops 0.500 m, and widens to 4.00 cm in diameter, the pressure would change due to the change in elevation and hose diameter. According to the principle of conservation of energy and assuming an ideal fluid (without losses), the pressure would increase as the hose's elevation decreases and cross-sectional area increases.