Final answer:
The highest absolute pressure in the hose at the location of the bend can be calculated using Bernoulli's equation, considering that the water speed increases and the pressure in the nozzle equals the atmospheric pressure. The calculation would involve rearranging Bernoulli's equation to solve for the initial pressure, given the known values for nozzle pressure, initial and final velocities, and the fluid density.
Step-by-step explanation:
To calculate the highest absolute pressure in a garden hose at the bend where cavitation occurs, we must consider the principle of conservation of energy for fluid flow, known as Bernoulli's equation. Given the information that the velocity of water increases from 1.96 m/s to 25.5 m/s, we can apply the equation to find the pressure in the hose before the nozzle. In this scenario, the absolute pressure in the nozzle is 1.01 × 105 N/m², which is atmospheric pressure.
Applying Bernoulli's equation,
P1 + ½ρv12 = P2 + ½ρv22,
where P is the pressure, ρ is the fluid density, and v is the fluid velocity. The subscripts 1 and 2 refer to the points before and at the nozzle, respectively. Since P2 is atmospheric pressure and v2 is greater than v1, P1 must be greater than P2.
Without the numerical density value (ρ) of water at 25°C, we cannot calculate the exact pressure. However, the equation above would typically allow us to find the absolute pressure in the hose before the nozzle. It would involve rearranging the equation to solve for P1 and inserting the known values for P2, v1, v2, and ρ.
It's important to note that this method assumes a frictionless flow and that the height of the fluid remains constant throughout the hose, so no potential energy term is needed in Bernoulli's equation.