Calculating the Speed of Water Entering the Hose

Oct 13, 2025 by leolavanderia.com.br 116 views

A hosepipe with a diameter of 4 cm is used to fill a 40-litre container. It takes 2 minutes to fill the container.

Calculating the Speed of Water Entering the Hose

In this problem, we are given a hosepipe with a diameter of 4 cm, used to fill a 40-litre container. The time taken to fill the container is 2 minutes. We need to calculate the speed at which the water enters the hose.

Understanding the Problem

To solve this problem, we need to understand the concept of flow rate and speed. The flow rate is the volume of fluid that flows through a given area in a given time. In this case, the flow rate is 40 litres per 2 minutes, which can be converted to litres per second.

Converting the Flow Rate

First, we need to convert the flow rate from litres per 2 minutes to litres per second. There are 60 seconds in 1 minute, so there are 120 seconds in 2 minutes.

# Import necessary modules
import math
flow_rate_litres_per_2_minutes = 40
seconds_in_2_minutes = 120
flow_rate_litres_per_second = flow_rate_litres_per_2_minutes / seconds_in_2_minutes

Calculating the Speed of Water Entering the Hose

Now that we have the flow rate in litres per second, we can calculate the speed of water entering the hose. The speed of water is given by the formula:

Speed = Flow rate / Area

The area of the hose can be calculated using the formula for the area of a circle:

Area = πr^2

where r is the radius of the hose.

# Define variables
diameter_hose = 4  # in cm
radius_hose = diameter_hose / 2  # in cm
area_hose = math.pi * (radius_hose ** 2)  # in cm^2
area_hose_m2 = area_hose * (10 ** -4)  # in m^2
speed_water = flow_rate_litres_per_second / area_hose_m2

Calculating the Speed of Water Entering the Hose in m/s

Now that we have the speed of water entering the hose in m/s, we can calculate the numerical value.

# Calculate numerical value of speed
speed_water_m_per_s = speed_water

Conclusion

In this problem, we calculated the speed of water entering a hose with a diameter of 4 cm, used to fill a 40-litre container. The time taken to fill the container is 2 minutes. We converted the flow rate from litres per 2 minutes to litres per second and then calculated the speed of water entering the hose using the formula: Speed = Flow rate / Area.

Final Answer

The final answer is: 0.25 m/s

Discussion

This problem is a classic example of a fluid dynamics problem. The speed of water entering the hose is an important parameter in many engineering applications, such as designing pipes and pumps.

Related Topics

Fluid dynamics
Flow rate
Speed of water
Area of a circle
Conversion of units

References

[1] "Fluid Dynamics" by Frank M. White
[2] "Mechanics of Fluids" by Merle C. Potter and David C. Wiggert

Additional Resources

[1] "Fluid Dynamics Tutorial" by Khan Academy
[2] "Mechanics of Fluids Tutorial" by MIT OpenCourseWare
A hosepipe with a diameter of 4 cm is used to fill a 40-litre container. It takes 2 minutes to fill the container.

Calculating the Speed of Water Entering the Hose

Q&A: Calculating the Speed of Water Entering the Hose

Q: What is the flow rate of the hose?

A: The flow rate of the hose is 40 litres per 2 minutes.

Q: How do I convert the flow rate from litres per 2 minutes to litres per second?

A: To convert the flow rate from litres per 2 minutes to litres per second, you need to divide the flow rate by the number of seconds in 2 minutes. There are 60 seconds in 1 minute, so there are 120 seconds in 2 minutes.

# Import necessary modules
import math
flow_rate_litres_per_2_minutes = 40
seconds_in_2_minutes = 120
flow_rate_litres_per_second = flow_rate_litres_per_2_minutes / seconds_in_2_minutes

Q: What is the area of the hose?

A: The area of the hose can be calculated using the formula for the area of a circle:

Area = πr^2

where r is the radius of the hose.

# Define variables
diameter_hose = 4  # in cm
radius_hose = diameter_hose / 2  # in cm
area_hose = math.pi * (radius_hose ** 2)  # in cm^2
area_hose_m2 = area_hose * (10 ** -4)  # in m^2

Q: How do I calculate the speed of water entering the hose?

A: The speed of water entering the hose can be calculated using the formula:

Speed = Flow rate / Area

# Calculate speed of water entering the hose
speed_water = flow_rate_litres_per_second / area_hose_m2

Q: What is the speed of water entering the hose in m/s?

A: The speed of water entering the hose in m/s is calculated by dividing the flow rate by the area of the hose.

# Calculate numerical value of speed
speed_water_m_per_s = speed_water

Q: What is the final answer?

A: The final answer is: 0.25 m/s

Q: What are some related topics?

A: Some related topics include:

Fluid dynamics
Flow rate
Speed of water
Area of a circle
Conversion of units

Q: What are some additional resources?

A: Some additional resources include:

[1] "Fluid Dynamics Tutorial" by Khan Academy
[2] "Mechanics of Fluids Tutorial" by MIT OpenCourseWare

Q: What are some references?

A: Some references include:

[1] "Fluid Dynamics" by Frank M. White
[2] "Mechanics of Fluids" by Merle C. Potter and David C. Wiggert

Conclusion

In this article, we have calculated the speed of water entering a hose with a diameter of 4 cm, used to fill a 40-litre container. The time taken to fill the container is 2 minutes. We have converted the flow rate from litres per 2 minutes to litres per second and then calculated the speed of water entering the hose using the formula: Speed = Flow rate / Area.

Final Answer

The final answer is: 0.25 m/s

Discussion

This problem is a classic example of a fluid dynamics problem. The speed of water entering the hose is an important parameter in many engineering applications, such as designing pipes and pumps.

Related Topics

Fluid dynamics
Flow rate
Speed of water
Area of a circle
Conversion of units

References

[1] "Fluid Dynamics" by Frank M. White
[2] "Mechanics of Fluids" by Merle C. Potter and David C. Wiggert

Additional Resources

[1] "Fluid Dynamics Tutorial" by Khan Academy
[2] "Mechanics of Fluids Tutorial" by MIT OpenCourseWare