Question

The heat flux, q, from a hot body in a stationary fluid is known to be a function of the fluid’s thermal conductivity k, and kinematic viscosity, ν, the temperature difference ΔT , the length of the object L, and the product of the local gravitational constant and the thermal expansion coefficient for the fluid, gβ. Determine the number of Pi groups thatcan be formed from these six parameters.

Answer 1

The number of pi groups are P = 3 pi groups

Step-by-step explanation:

From the question we are told that

The number of parameters is n = 6

These parameters are : Fluid thermal conductivity : k

Kinematic viscosity: v

The temperature difference ΔT

The length of the object L

Gravitational constant g

Thermal expansion coefficient β

The number of the basic dimensional unit is N = 3

Mass M

Length L

Time T

Generally the number of Pi groups is mathematically evaluated as

P = n - N

=> P = 6 - 3

=> P = 3 pi groups