Final answer:
To calculate the flow rate in liters per second, multiply the velocity by the cross-sectional area of the hose and convert from m^3/s to L/s. To find the nozzle's inside diameter, use the given fluid velocity and the same formula to calculate the cross-sectional area.
Step-by-step explanation:
Step 1: Convert the given velocity from m/s to L/s.
The flow rate can be calculated by multiplying the velocity by the cross-sectional area of the hose. The cross-sectional area of the hose can be found using the formula:
Area = π * (diameter/2)^2
Substituting the given values:
Area = π * (1.60 cm/2)^2 = π * (0.80 cm)^2 = 2.01 cm^2
Converting the area from cm^2 to m^2:
2.01 cm^2 * (0.01 m/cm)^2 = 0.000201 m^2
Now, multiply the velocity by the area to find the flow rate:
Flow Rate = 2.00 m/s * 0.000201 m^2 = 0.000402 m^3/s
To convert the flow rate from m^3/s to L/s, multiply by 1000:
Flow Rate = 0.000402 m^3/s * 1000 L/m^3 = 0.402 L/s
Step 2: Determine the nozzle's inside diameter using the fluid velocity.
Using the same formula as before to find the cross-sectional area of the nozzle:
Area = π * (diameter/2)^2
Substituting the given values:
Area = π * (diameter/2)^2 = π * (diameter/2)^2 = π * (0.80 cm)^2
Solve for the diameter:
(0.80 cm)^2 = (diameter/2)^2
diameter/2 = sqrt((0.80 cm)^2)
diameter = 2 * sqrt((0.80 cm)^2)