Question

A liquid of density 1310 kg/m�� flows steadily through a pipe of varying diameter and height. At location 1 along the pipe, the flow speed is 9.89 m/s and the pipe diameter is ________.

Answer 1

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.