1

Determining the P groupsModule 22Reading in Fox & McDonald, pgs. 297 - 298

2

How do we determine the dimensionless groups for a given process? (pgs. 297 – 298)

There is a series of steps that you should follow to determine the dimensionless groups for a given process.

Go through steps with example….

3

How do we determine the dimensionless groups for a given process?

F = f(r, V, D, m)

Step 1: List all dimensional parameters involved.

4

How do we determine the dimensionless groups for a given process?

Step 2: Select a set of fundamental dimensions.

5

How do we determine the dimensionless groups for a given process?

Step 3: List the dimensions of all parameters in terms of primary dimensions.

6

How do we determine the dimensionless groups for a given process?

Step 4: Select a set of r dimensional parameters that include all the primary dimensions.

7

How do we determine the dimensionless groups for a given process?

Step 5: Set up dimensional equations, combining the parameters selected in Step 4 with each of the other parameters in turn, to form dimensionless groups.

8

How do we determine the dimensionless groups for a given process?

Step 5: Set up dimensional equations, combining the parameters selected in Step 4 with each of the other parameters in turn, to form dimensionless groups.

9

How do we determine the dimensionless groups for a given process?

Step 6: Check to see that each group obtained is dimensionless.

10

Determining the P groupsGroup work

The thrust, T, developed by a propeller of a given shape depends on its diameter, D, the fluid density, r, the viscosity, m, the angular speed rotation, w, and the advance velocity, V. Develop a suitable set of Pi terms.

11

Determining the P groups

12

Determining the P groups

13

Determining the P groups

14

Determining the P groups