Calculate Kinematic Viscosity for Stirred Tank System

[db725]

Homework Statement

The liquid in a production stirred tank system in which vortexing occurs has viscosity equal to 0.005 Pas and density equal to 900 kg m^3. A 1/5th scale laboratory model of the production unit is built to investigate the mixing performance. The liquid used in the laboratory model is chosen to ensure dynamic similarity on both Reynolds Number and Froude Number. Calculate the kinematic viscosity required for the laboratory liquid. Give units for your numerical answer.

Homework Equations

v : kinematic viscosity, v1 : laboratory kinematic viscosity, v2: production kinematic viscosity
μ : dynamic viscosity
ρ : density of the liquid
d : diameter of stirrer, d1: diameter of laboratory, d2: diameter of production

v=μ/ρ

v1/v2= (d1/d2)^2

The Attempt at a Solution

v1/(0.0005/900)= [(1/5)/(1)]^2 so v1= 72 000 (not sure about the units ??)

my attempt to the units are as below:

kg/m^3 x 1/(Pa.s) =kg/(mxN.s)

Can someone help? is this the right answer with the units included?

Thanks in advance for the help

 

[KataKoniK]

.
Thank you for your post. Your attempt at solving the problem is correct, but there are a few units that need to be clarified.

Firstly, the units for kinematic viscosity are m^2/s. This can be derived from the equation v=μ/ρ, where μ has units of Pa.s (Pascal-seconds) and ρ has units of kg/m^3 (kilograms per cubic meter). When you divide Pa.s by kg/m^3, you get m^2/s.

In your calculation, the units for v1 should be m^2/s, and the units for v2 should be (0.005 Pa.s)/(900 kg/m^3) = 5.56 x 10^-6 m^2/s.

Therefore, the units for v1/v2 should be (m^2/s)/(m^2/s) = 1.

Using the second equation, v1/v2= (d1/d2)^2, we can rewrite it as v1= (d1/d2)^2 x v2. Since we know that d1/d2 = 1/5, we can substitute this value in and get v1= (1/5)^2 x (5.56 x 10^-6 m^2/s) = 2.78 x 10^-7 m^2/s.

Therefore, the kinematic viscosity required for the laboratory liquid is 2.78 x 10^-7 m^2/s.

I hope this helps. Please let me know if you have any further questions.