Water is ejected from a garden hose of radius 1.06 cm at a speed of 5.19 m/s. Find the flow rate through the hose.
To find the flow rate through the hose, we need to calculate the volume of water being ejected per unit time.
The flow rate can be calculated using the formula:
Flow rate = Cross-sectional area × Velocity
First, we need to find the cross-sectional area of the hose. Since the hose has a circular cross-section, we can use the formula for the area of a circle:
Area = π × radius^2
Given that the radius of the hose is 1.06 cm, we convert it to meters by dividing by 100:
radius = 1.06 cm ÷ 100 = 0.0106 m
Now, we can calculate the cross-sectional area:
Area = π × (0.0106 m)^2
Next, we need to calculate the flow rate by multiplying the cross-sectional area by the velocity of the water:
Flow rate = Area × Velocity
Substituting the values, we get:
Flow rate = π × (0.0106 m)^2 × 5.19 m/s
Finally, we can calculate the flow rate through the hose using a calculator:
Flow rate ≈ 0.000183 m^3/s
Therefore, the flow rate through the hose is approximately 0.000183 cubic meters per second.