Final answer:
The flow rate of water through the hose is 0.402 liters per second. The inside diameter of the nozzle is 0.25 cm.
Step-by-step explanation:
To calculate the flow rate of water through a hose, we can use the equation:
Flow rate = velocity x cross-sectional area
Given that the velocity is 2.00 m/s and the diameter is 1.60 cm, we need to convert the diameter to meters:
Diameter = 1.60 cm = 0.016 m
The cross-sectional area can be calculated using the formula:
Area = pi x (radius)^2
Radius = (diameter / 2) = 0.016 / 2 = 0.008 m
Now, we can calculate the area:
Area = pi x (0.008)^2 = 0.000201 m^2
Finally, we can calculate the flow rate:
Flow rate = 2.00 m/s x 0.000201 m^2 = 0.000402 m^3/s
Since 1 liter is equal to 0.001 cubic meters, the flow rate in liters per second is:
Flow rate = 0.000402 m^3/s x (1 L / 0.001 m^3) = 0.402 L/s
Therefore, the flow rate of water through the hose is 0.402 liters per second.
To calculate the inside diameter of the nozzle, we can rearrange the equation:
Flow rate = velocity x cross-sectional area
Given that the flow rate is 0.402 L/s and the velocity is 15.0 m/s, we need to convert the flow rate to cubic meters per second:
Flow rate = 0.402 L/s x 0.001 m^3/L = 0.000402 m^3/s
The cross-sectional area can be calculated using the formula:
Area = flow rate / velocity
Area = 0.000402 m^3/s / 15.0 m/s = 0.0000268 m^2
Now, we can calculate the diameter using the formula:
Diameter = 2 x square root(area / pi)
Diameter = 2 x square root(0.0000268 m^2 / pi) = 0.0025 m = 0.25 cm
Therefore, the inside diameter of the nozzle is 0.25 cm.