Question

A garden hose with a diameter of 2.0 cm is used to fill a bucket, which has a volume of 0.10 cubic meters. It takes 1.2 minutes to fill. An adjustable nozzle is attached to the hose to decrease the diameter of the opening, which increases the speed of the water. The hose is held level to the ground at a height of 1.0 meters, and the diameter is decreased until a flower bed 3.0 meters away is reached.

(a) What is the volume flow rate of the water through the nozzle when the diameter is 2.0 cm?
(b) What is the speed of the water coming out of the hose?
(c) What does the speed of the water coming out of the hose need to be to reach the flower bed 3.0 meters away?
(d) What is the diameter of the nozzle needed to reach the flower bed?

Answer 1

The volume flow rate of water through the nozzle can be calculated using the formula: Q = A * v. The speed of the water can be calculated using the equation of continuity: A1 * v1 = A2 * v2. To find the speed of the water needed to reach the flower bed, we can use the equation: v = d / t. The diameter of the nozzle needed to reach the flower bed can be found using the equation: D = 2 * r.

Step-by-step explanation:

The volume flow rate of water through the nozzle can be calculated using the formula:

Q = A * v

Where Q is the flow rate, A is the cross-sectional area of the nozzle, and v is the speed of the water. The cross-sectional area of the nozzle can be calculated using the formula:

A = π * r^2

Where A is the cross-sectional area and r is the radius of the nozzle.

To find the speed of the water coming out of the hose, we can use the equation of continuity:

A1 * v1 = A2 * v2

Where A1 is the cross-sectional area of the hose, v1 is the speed of the water in the hose, A2 is the cross-sectional area of the nozzle, and v2 is the speed of the water in the nozzle.

To calculate the speed of the water needed to reach the flower bed 3.0 meters away, we can use the equation:

v = d / t

Where v is the speed of the water, d is the distance to the flower bed, and t is the time taken.

Finally, to find the diameter of the nozzle needed to reach the flower bed, we can use the equation:

D = 2 * r

Where D is the diameter of the nozzle and r is the radius of the nozzle.