Final answer:
To calculate the speed of the water in the nozzle, we can use the relationship between flow rate and speed. The flow rate through the hose and nozzle is given as 0.469 L/s.
Step-by-step explanation:
To calculate the speed of the water in the nozzle, we can use the relationship between flow rate and speed.
The flow rate through the hose and nozzle is given as 0.469 L/s.
We can calculate the speed of the water in the nozzle using the formula v = Q/A, where v is the speed, Q is the flow rate, and A is the cross-sectional area of the nozzle.
The cross-sectional area of the nozzle can be calculated using the formula A = πr^2, where r is the radius of the nozzle.
Given that the radius of the nozzle is 0.596 cm, we can convert it to meters by dividing by 100.
So, the radius of the nozzle is 0.00596 m.
Substituting the values into the formula,
A = π(0.00596)^2
= 1.118 x 10^-4 m^2.
Now, we can use the formula v = Q/A to calculate the speed of the water in the nozzle.
Substituting the values,
v = 0.469 / 1.118 x 10^-4
= 4190.5 m/s.