A company manufacturing pvc pipes claims in an advertisement that the volume of water flowing out through the pipe in a given time is as per the equation v = ka2 ut where a is the area of cross section of the pipe, u is the speed of flow, t is the time and k is a dimensionless constant.
a.name the principle that can be used to check the dimensional correctness of this equation.
b.check the equation and state whether the claim can be correct
Answers
a) principle of homogeneity b) keep the dimensional formulas on both sides of equation. if L.H.S=R.H.S ; the formula is correct. Ans. the formula is not correct
A. The principle that can be used to check the dimensional correctness of this equation is called the Principle of Homogeneity.
B. The claim is not correct.
Given:
The equation V = KA²ut.
To Find:
A. Name the principle that can be used to check the dimensional correctness of this equation.
B. Check the equation and state whether the claim can be correct.
Solution:
A. The principle that can be used to check the dimensional correctness of this equation is called the Principle of Homogeneity.
B. As we know that the Principle of Homogeneity states that - the dimensions of the terms on the left-hand side should be equal to the dimensions on the right-hand side.
Hence, if we check the dimensions of the left-hand side of the given equation, that is V whose dimension is equal to [L³].
And the dimensions of the terms on the right-hand side are equal to [A]² = [L²]² = [L]⁴ and [u] = [LT⁻¹] and [t] = [T].
Hence, [KA²ut] = [L]⁴ [LT⁻¹] [T] = [L]⁵.
As we can see that the dimensions of the right-hand side and the left-hand side are not equal
Hence, we can conclude that the claim is not correct.
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