To find the diameter of the nozzle, we can use the equation of continuity, which states that the flow rate (volume per unit time) is constant. This means that the product of the cross-sectional area and the velocity is the same at any point in the hose or nozzle.

$$Q1=Q2$$

$$A1v1=A2v2$$

$$(\pi d1 ^2/4)v1=(\pi d2^2/4)v2$$

Where:

Q1 is the flow rate at the hose

Q2 is the flow rate at the nozzle

A1 is the cross-sectional area of the hose

A2 is the cross-sectional area of the nozzle

d1 is the diameter of the hose

d2 is the diameter of the nozzle

v1 is the velocity of the water in the hose

v2 is the velocity of the water at the nozzle

Rearranging the equation to solve for d2, we get:

$$d2=\sqrt{d1^2 \frac{v1}{v2}}$$

Substituting the given values:

$$d2=\sqrt{(1.85 \ cm)^2 \frac{860 \ cm^3/s}{10.8 \ m/s}}$$

$$d2=0.53 \ cm$$

Therefore, the diameter of the nozzle is 0.53 cm.