Find the primary dimensions of each of the following terms. a. (pV2)/2 (kinetic pressure), where p is fluid density and V is velocity b. T (torque) c. P (power) d. (PV2L)/ (Weber number), where p is fluid density, V is velocity, L is length, and is surface tension.
In order to determine the primary dimension of the term under the section we will consider the base units for every variable. Since the unit used for the density is:
Therefore, we can write the primary dimension for the density, using the relation between the signs and the dimensions of given base units as:
The unit used for the velocity is:
We are going to write the primary dimension for the velocity, using the relation between the signs and the dimensions of given base units as:
Finally we are able to determine the primary dimension of the kinetic pressure as:
Recommended textbook solutions
Oil with a density of and kinematic viscosity of is being discharged by a 8-mm-diameter, 40-m-long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 4 m. Disregarding the minor losses, determine the flow rate of oil through the pipe.