A Hosepipe With A Diameter Of 4 Cm Is Used To Fill A 40-litre Container. It Takes 2 Minutes To Fill The Container. A) Calculate The Speed At Which The Water Enters The Hose.
Introduction
In this article, we will explore the concept of calculating the speed at which water enters a hosepipe. We will use a real-world scenario to demonstrate how to apply mathematical principles to solve a problem. The scenario involves a hosepipe with a diameter of 4 cm being used to fill a 40-litre container in 2 minutes.
Understanding the Problem
To calculate the speed at which water enters the hosepipe, we need to understand the concept of flow rate. Flow rate is the volume of fluid that flows through a given area in a given time. In this case, we are given the volume of the container (40 litres) and the time it takes to fill the container (2 minutes). We need to calculate the speed at which the water enters the hosepipe.
Calculating the Flow Rate
To calculate the flow rate, we need to use the formula:
Flow rate = Volume / Time
In this case, the volume is 40 litres and the time is 2 minutes. We need to convert the time from minutes to seconds, as the standard unit of time in the International System of Units (SI) is the second.
1 minute = 60 seconds 2 minutes = 120 seconds
Now, we can plug in the values into the formula:
Flow rate = 40 litres / 120 seconds Flow rate = 0.333 litres/second
Calculating the Speed of Water Entry
To calculate the speed at which the water enters the hosepipe, we need to use the formula:
Speed = Flow rate / Area
We need to calculate the area of the hosepipe. The formula for the area of a circle is:
Area = πr^2
where r is the radius of the circle. The diameter of the hosepipe is 4 cm, so the radius is half of the diameter:
r = 4 cm / 2 r = 2 cm
Now, we can plug in the values into the formula:
Area = π(2 cm)^2 Area = 12.57 cm^2
Now, we can plug in the values into the formula:
Speed = 0.333 litres/second / 12.57 cm^2 Speed = 0.0265 m/s
Converting the Speed to a More Meaningful Unit
The speed we calculated is in metres per second (m/s). However, this unit may not be very meaningful in this context. A more meaningful unit would be litres per minute (L/min). We can convert the speed from m/s to L/min by multiplying it by 60 (since there are 60 seconds in a minute):
Speed = 0.0265 m/s x 60 Speed = 1.59 L/min
Conclusion
In this article, we calculated the speed at which water enters a hosepipe with a diameter of 4 cm. We used the formula for flow rate and the formula for the area of a circle to calculate the speed. We also converted the speed from metres per second to litres per minute to make it more meaningful. The speed at which water enters the hosepipe is approximately 1.59 L/min.
Mathematical Formulas Used
- Flow rate = Volume / Time
- Area = πr^2
- Speed = Flow rate / Area
References
- International System of Units (SI). (2019). The International System of Units (SI).
- Wikipedia. (2023). Flow rate.
A Hosepipe Filling a Container: Calculating Water Flow Rate - Q&A ================================================================
Introduction
In our previous article, we explored the concept of calculating the speed at which water enters a hosepipe. We used a real-world scenario to demonstrate how to apply mathematical principles to solve a problem. In this article, we will answer some frequently asked questions related to the topic.
Q&A
Q: What is the formula for calculating the flow rate?
A: The formula for calculating the flow rate is:
Flow rate = Volume / Time
Q: What is the unit of flow rate?
A: The unit of flow rate is typically measured in litres per second (L/s) or cubic metres per second (m^3/s).
Q: How do I convert the flow rate from litres per second to litres per minute?
A: To convert the flow rate from litres per second to litres per minute, you can multiply the flow rate by 60 (since there are 60 seconds in a minute).
Q: What is the formula for calculating the area of a circle?
A: The formula for calculating the area of a circle is:
Area = πr^2
where r is the radius of the circle.
Q: How do I calculate the speed of water entry into the hosepipe?
A: To calculate the speed of water entry into the hosepipe, you can use the formula:
Speed = Flow rate / Area
Q: What is the unit of speed?
A: The unit of speed is typically measured in metres per second (m/s) or litres per minute (L/min).
Q: Can I use a different unit of measurement for the diameter of the hosepipe?
A: Yes, you can use a different unit of measurement for the diameter of the hosepipe, such as centimetres (cm) or millimetres (mm). However, make sure to convert the unit to the same unit as the radius.
Q: How do I calculate the volume of the container?
A: To calculate the volume of the container, you can use the formula:
Volume = Area x Height
where Area is the cross-sectional area of the container and Height is the height of the container.
Q: What is the relationship between flow rate and pressure?
A: The flow rate is directly proportional to the pressure difference between the two ends of the hosepipe. This means that if the pressure difference increases, the flow rate will also increase.
Q: Can I use this method to calculate the flow rate of a pipe with a non-circular cross-section?
A: No, this method is only applicable to pipes with a circular cross-section. For pipes with a non-circular cross-section, you will need to use a different method to calculate the flow rate.
Conclusion
In this article, we answered some frequently asked questions related to calculating the speed at which water enters a hosepipe. We covered topics such as flow rate, area, speed, and pressure. We hope that this article has provided you with a better understanding of the topic and has helped you to answer any questions you may have had.
Mathematical Formulas Used
- Flow rate = Volume / Time
- Area = πr^2
- Speed = Flow rate / Area
- Volume = Area x Height
References
- International System of Units (SI). (2019). The International System of Units (SI).
- Wikipedia. (2023). Flow rate.