Question

Find the dimension of the quantity v in the equation
v = {πP(a2 – x2) } / (2ηL)
where a is the radius and L length of the tube in which the fluid of coefficient of viscosity η is flowing, x is the distance from the axis and P is the pressure difference​

Answer 1

dimension of v is [LT¯¹]

we have to find the dimension of the quantity v in the equation, v = {πP(a² - x²)}/2ηL

where a is the radius , L length of the tube in which the fluid of coefficient of viscosity η is flowing, x is the distance from the axis and P is the pressure difference.

• dimension of P = [M¹L¯¹T¯²]
• dimension of a/x/L = [L]
• dimension of η = [M¹L¯¹T¯¹]

now, dimension of v = dimension of P × dimension of a² or x²/{dimension of η × dimension of L}

= [M¹L¯¹T¯²] [L²]/{[M¹L¯¹T¯¹][L]}

= [LT¯¹]

therefore, dimension of v is [LT¯¹]

Answer 2

dimension of v = dimension of P × dimension of a² or x²/{dimension of η × dimension of L}

= [M¹L¯¹T¯²] [L²]/{[M¹L¯¹T¯¹][L]}

= [LT¯¹]