2, A garden hose of inner diameter 2.0 cm carries water at 2.0m/s The nozzle at the end has diameter 0.4 cm. how fast does the water move through the nozzle ? Ans: 50m/s

## Step 1: Identify the Problem### We are given a problem dealing with the flow of water through a garden hose and a nozzle. The principle that applies here is the equation of continuity in fluid dynamics. This equation states that the product of the cross-sectional area ( ) of a pipe and the velocity ( ) of the fluid flow remains constant.## Step 2: Convert Diameters to Radii### The inner diameter of the garden hose is , so the radius is or . The diameter of the nozzle is , so the radius is or .## Step 3: Calculate Cross-Sectional Areas### The cross-sectional area of a tube or pipe is calculated as . Therefore, the areas are: ## Step 4: Apply the Equation of Continuity### The equation of continuity is . We need to solve for : Substituting the areas: ## Step 5: Simplify and Solve### Simplifying the expression: