If a solution with 50% one fluid 50% another flowing through a pipe, with a give

ID: 2086545 • Letter: I

Question

If a solution with 50% one fluid 50% another flowing through a pipe, with a given temperature, and internal diameter of pipe and pressure gradient per metre.
How would you confirm the flow is laminar ?
Calculate the volumetric flow rate ?
And calculate the local velocity of liquid at a given perpendicular distance from the inner wall of the pipe ? If a solution with 50% one fluid 50% another flowing through a pipe, with a given temperature, and internal diameter of pipe and pressure gradient per metre.
How would you confirm the flow is laminar ?
Calculate the volumetric flow rate ?
And calculate the local velocity of liquid at a given perpendicular distance from the inner wall of the pipe ?
How would you confirm the flow is laminar ?
Calculate the volumetric flow rate ?
And calculate the local velocity of liquid at a given perpendicular distance from the inner wall of the pipe ?

Explanation / Answer

(a) To determine laminar flow:

Let average density of the mixture = ? and length of the pipe = L

The average density of mixture can be found by the equation, 1/? = (0.5/?1 + 0.5/?2) = 0.5(1/?1 + 1/?2); where ?1 and ?2 are densities of 1st and 2nd fluids respectively.

Internal diameter = d, Pressure gradient = dp/dl

For laminar flow, average velocity of fluid inside pipe, uavg = -(1/8?)*(dp/dL)*(d/2)2 … (i)

Where, ? = viscosity of fluid.

From equation (i) the value of uavg can be found out.

Reynold’s number, Re = (?*uavg*d)/? …(ii)

From equation (ii) the value of Re can be found out. If Re < 2000, then the flow is laminar.

(b) Calculating the volumetric flow rate:

Area of pipe cross section, A = (?/4)*d2

Hence, volumetric flow rate, q = uavg*A = uavg*(?/4)*d2

(d) Calculating local velocity at any distance from inner wall of pipe:

For laminar flow, velocity of fluid at a perpendicular distance ‘r’ from the inner wall of the pipe,

ur = -(1/4?)*(dp/dL)*[(d/2)2 – r2]…(iii)

The equation (iii) will provide the local velocity of liquid at a given perpendicular distance from the inner wall of the pipe.

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