check the accuracy of the relation
v=πPr⁴/8nl
.....where v is the volume per unit time ,p is the pressure,r is the radous ,n is the coefficient of viscosity and l is the length
Solve it ......
Answers
we have to check the accuracy of the relation,
v = πPr⁴/8ηl
where v is the volume per unit time, p is the pressure, r is the radius, η is the coefficient of viscosity and l is the length.
solution : first consider dimensional formula of each term.
v = volume/time = [L³T¯¹]
p = pressure = force/area = [ML¯¹T¯²]
r = radius = [L]
η = coefficient of viscosity = [ML¯¹T¯¹]
l = length = [L]
LHS = v = [L³T¯¹]
RHS = πPr⁴/8ηl = [ML¯¹T¯²][L⁴]/[ML¯¹T¯¹][L]
= [ML³T¯²]/[MT¯¹]
= [L³T¯¹]
here LHS = RHS
hence relation v = πPr⁴/8ηl, is dimensionally correct.
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Answer:
it is dimensionally correct.