Question

check the accuracy of the relation
η=π/8 Pr⁴/lV
where, P is pressure, V= rate of liquid through a pipe, η is coefficient of viscosity of liquid, l is length​

Answer 1

Answer:

Explanation: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.