Question

How many litres of water will flow in $ 7 $ minutes from a cylindrical pipe $ 1 $ cm in diameter, if the water flows at a speed of $ 30 $ km per hour?

Answer 1

Hint: First of all find the volume of the cylindrical pipe and before that convert the measure of diameter in meter first and then convert it in radius and then simplify placing in the formula and since resultant volume would be cubic meter and therefore at last convert the meter cube in liters.

Complete step by step solution:
Given that: Diameter of the cylindrical pipe, $ d = 1cm $
Radius is given by dividing diameter by the number two.
Radius, $ r = \dfrac{d}{2} $
  $ r = \dfrac{1}{2} $ cm
 $ r = 0.5 \times {10^{ - 2}} $ m
Speed of water flows $ = 30km/hr $
Convert in the same format of the unit.
Speed of water flows $ = \dfrac{{30 \times 1000}}{{3600}}m/s $
The water flows $ \dfrac{{30 \times 1000}}{{3600}}m $ in one second
Therefore, water flows in $ 7 $ minutes $ = \dfrac{{30 \times 1000}}{{3600}} \times 7 \times 60m $
Common factors from the numerator and the denominator cancel each other.
water flows in $ 7 $ minutes $ = 3500m $
So, the length of the meters of the water flow is the height of the cylindrical pipe.
Therefore, height $ h = 3500m $
Now, the volume of water flow in $ 7 $ minutes $ V = \pi {r^2}h $
Place the values in the above expression –
 $ V = \dfrac{{22}}{7}{(0.5 \times {10^{ - 2}})^2} \times 3500 $
Simplify the above expression by removing the common factors from the numerator and the denominator.
 $ V = 22 \times 0.5 \times 0.5 \times {10^{ - 4}} \times 5 $
Simplify the above expression finding the product of the terms –
 $ V = 27.5 \times {10^{ - 4}}{m^3} $
Convert the cubic meter in terms of liters –
Convert cubic meters in litres.
 $ 1{m^3} = 1000{\text{ }}litres $ -
 $ V = 27.5 \times {10^{ - 4}} \times 1000 $
Simplify the above expression –
 $ V = 275 $ liters
Hence, the $ 275 $ litres of water will flow in $ 7 $ minutes from a cylindrical pipe.
So, the correct answer is “275 Liters”.

Note: The most important here is the standard formula and its application along with its simplification. Always remember the basic conversion relations and convert them as per the need. Remember the difference among the units such as one meter and one centimetre both gives us the measure of length, and so before placing any values in the formula check all the terms should be in the same system of units.