Final answer:
The pressure drop due to the Bernoulli effect can be calculated using the formula ΔP = P1 - P2 = ½ρ(V2² - V1²), where ΔP is the pressure drop, P1 is the pressure at the fire hose, P2 is the pressure at the nozzle, ρ is the density of the fluid, V1 is the velocity of the fluid at the fire hose, and V2 is the velocity of the fluid at the nozzle. To calculate the maximum height the water can rise, we can use the principle of conservation of energy with the equation PE = mgh, where PE is the potential energy, m is the mass of the water, g is the acceleration due to gravity, and h is the height.
Step-by-step explanation:
To calculate the pressure drop due to the Bernoulli effect, we can use Bernoulli's equation. Bernoulli's equation states that the sum of the pressure, kinetic energy, and potential energy per unit volume of a fluid is constant along a streamline. In this case, the pressure drop can be calculated by subtracting the pressure at the nozzle from the pressure at the fire hose. The pressure drop is given by the formula ΔP = P1 - P2 = ½ρ(V2² - V1²), where ΔP is the pressure drop, P1 is the pressure at the fire hose, P2 is the pressure at the nozzle, ρ is the density of the fluid, V1 is the velocity of the fluid at the fire hose, and V2 is the velocity of the fluid at the nozzle.
To calculate the maximum height the water can rise, we can use the principle of conservation of energy. The potential energy of the water at the maximum height is equal to the kinetic energy it had at the nozzle. The potential energy can be calculated using the formula PE = mgh, where PE is the potential energy, m is the mass of the water, g is the acceleration due to gravity, and h is the height. Setting the potential energy equal to the kinetic energy and solving for h will give us the maximum height.