The speed v of a liquid leaving a tube depends on the
change in pressure AP and the density p of the liquid. The
speed is given by the equation: v = k ) Where k is a
constant that has no units. What is the value of n?
(a) 1/2 (b) 1
(C) 3/2 (d) 2
Answers
The value of n will be a.) 1/2
Units of velocity = ms-1
The overall units of the right-hand side of the equation should also be ms¹ for the equation to be homogeneous.
k has no units and be neglected for dimension analysis.
Change in Pressure, ∆P = ∆hpg
So, ∆P/p=∆hpg/ p = ∆hg
Units of ∆P/p:
[∆P/p] = [∆hg] = m ms-2 = m²s-2
Consider the units: ms-1 = [m²s-2]½
Therefore, for the equation to be homogeneous, n should be ½.
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Answer: the value of n is (a) 1/2.
Explanation:
Units of velocity = ms-1
The overall units should be ms¹ for the equation to be homogeneous.
Change in Pressure, ∆P = ∆hpg
So, ∆P/p=∆hpg/ p = ∆hg
Units of ∆P/p= [∆P/p]
= [∆hg] = m ms-2
=m²s-2
Consider the units: ms-1 = [m²s-2]½
Hence, for the equation to be homogeneous, n should be ½.
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