(I) A gardener feels it is taking too long to water a garden with a in diameter hose. By
what factor will the time be cut using a in - diameter hose instead? Assume nothing else is changed cut using
We have to find by what factor would the time be reduce when it diameter of the hose is changed, keeping all other condition same.
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We assume that the streamlined flow of the water is not affected, by the change in diameter of the hose.As the same volume of water is used, therefore as we know that the time is inversely proportional to the rate of flow.
Also, from Poiseuille’s equation, we know that the rate of flow is proportional to the fourth power of the radius of the house.
Thus,the time is inversely proportional to the fourth power of the radius of the house.