Final answer:
To calculate the pressure in the hose, we can use Bernoulli's principle. Bernoulli's equation states that the total pressure, which is the sum of the static pressure and dynamic pressure, remains constant along a streamline. The pressure in the hose can be calculated using the equation P₁ = P₂ + (1/2)ρ(v₂² - v₁²), where P₁ is the pressure in the hose, P₂ is the absolute pressure in the nozzle, ρ is the density of water, and v₁ and v₂ are the speeds of water in the hose and nozzle respectively.
Step-by-step explanation:
To calculate the pressure in the hose, we can use Bernoulli's principle. Bernoulli's equation states that the total pressure, which is the sum of the static pressure and dynamic pressure, remains constant along a streamline.
In this case, the speed of water increases from 1.96 m/s to 25.5 m/s as it flows from the hose to the nozzle. Since the flow is level and frictionless, we can assume that the change in height is negligible. Therefore, the static pressure in the hose can be calculated using the equation:
P₁ = P₂ + (1/2)ρ(v₂² - v₁²)
where P₁ is the pressure in the hose, P₂ is the absolute pressure in the nozzle (1.01 × 10^5 N/m²), ρ is the density of water, and v₁ and v₂ are the speeds of water in the hose and nozzle respectively.
By substituting the given values and solving the equation, we can find the pressure in the hose.