Question

Suppose you spray your sister with water from a garden hose. The water is supplied to the hose at a rate of 0.433×10−3 m3/s0.433×10−3 m3/s and the diameter of the nozzle you hold is 5.855.85 × 10-3 m. At what speed does the water exit the nozzle

Answer 1

Answer:

$16.12$ m/s

Explanation:

$V$  = Volume flow rate of water through the hose = 0.433 x 10⁻³ m³

$d$ = diameter of nozzle = 5.85 x 10⁻³ m

Area of cross-section of nozzle is given as

$A = (0.25)\pi d^{2}$

$A = (0.25)(3.14) (5.85\times 10^{-3})^{2}$

$A = 26.86\times 10^{-6}$ m²

$v$ = speed of water exiting the nozzle

Using equation of continuity

$V = A v$

$0.433\times 10^{-3} = (26.86\times 10^{-6}) v$

$v = 16.12$ m/s

Answer 2

The exit speed of the water from the nozzle is 16.1 m/s.

Exit speed of the water

The exit speed of the water from the nozzle is determined by applying continuity equation as shown below;

Q = Av

where;

• A is the area of the nozzle
• Q is the flowrate
• v is speed of the water

Area of the nozzle is calculated as follows;

A = πd²/4 = π(5.85 x 10⁻³)²/4

A = 2.688 x 10⁻⁵ m²

Speed of water from the nozzle is calculated as follows;

v = Q/A

v = (0.433 x 10⁻³)/(2.688 x 10⁻⁵)

v = 16.1 m/s

Thus, the exit speed of the water from the nozzle is 16.1 m/s.

Learn more about flow rate here: https://brainly.com/question/21630019