Water running in a cylindrical pipe of inner diameter 7cm across a field, is collected by a farmer in a container at the rate of 192.5 litres per minute to avoid its wastage. Find the rate of flow of water in the pipe in km/hr. Take pie= 22/7?

Question

Answer

Answer

Answer

Flow rate = Volumetric flow rate/Area

Area = pi * r2  = (22/7)*7/2*7/2= 38.5 cm2

Volumetric flow rate = 192.5 l/min.

Since 1l = 1dm3 = 1000 cm3

So, Volumetric flow rate = 192.5 *1000  cm3/min

So, flow rate = 192.5 *1000  cm3/min / 38.5 cm2

  flow rate = = 5000 cm/min = 5000*0.00001 km/(1/60 h) = 3 km/h

Answer

The Problem:
A cylindrical pipe with an inner diameter of 7 cm is running water across a field. The farmer wants to collect the water to avoid wastage. The water is being collected at a rate of 192.5 litres per minute. We need to find the rate of flow of water in the pipe in km/hr, considering π=22/7.

The Approach:
To find the rate of flow of water in the pipe in km/hr, we need to convert the given rate of flow from litres per minute to cubic meters per hour. Then, we can convert the volume into distance by considering the area of the pipe's cross-section.

The Solution:

Step 1: Convert litres per minute to cubic meters per hour
- Given rate of flow = 192.5 litres per minute
- 1 litre = 0.001 cubic meters
- Therefore, 192.5 litres = 192.5 * 0.001 = 0.1925 cubic meters
- To convert minutes to hours, multiply by 60: 0.1925 * 60 = 11.55 cubic meters per hour

Step 2: Calculate the area of the pipe's cross-section
- The pipe is cylindrical with an inner diameter of 7 cm.
- The radius of the pipe (r) = diameter / 2 = 7 cm / 2 = 3.5 cm = 0.035 meters
- The area of the pipe's cross-section (A) = π * r^2
- Substituting the given value of π = 22/7 and r = 0.035 meters, we get:
A = (22/7) * (0.035)^2 = 0.00385 square meters

Step 3: Calculate the rate of flow in km/hr
- The volume of water flowing through the pipe in one hour is given by:
Volume = Rate * Time = 11.55 cubic meters per hour
- The distance traveled by the water in one hour is given by:
Distance = Volume / Area = 11.55 cubic meters / 0.00385 square meters
Distance = 3000 meters
- To convert the distance from meters to kilometers, divide by 1000:
Distance = 3000 / 1000 = 3 kilometers

Step 4: Final result
The rate of flow of water in the pipe is 3 km/hr.

Summary:
The rate of flow of water in the cylindrical pipe with an inner diameter of 7 cm is found to be 3 km/hr. This is calculated by converting the given rate of flow from litres per minute to cubic meters per hour, and then converting the volume into distance by considering the area of the pipe's cross-section.

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