Download Dim Reasoning Assignment

Dimensional Reasoning Problem Sheet
1. It is observed that the velocity v of a liquid leaving a nozzle depends upon the pressure drop P and the
density r. Show that the relationship between them is of the form:
2. It is observed that the speed of a sound a in a liquid depends upon the density r and the bulk modulus K
(the bulk modulus characterizes compressibility of a fluid – units of pressure). Show that the relationship
between them is:
3. It is observed that the frequency of oscillation f ([f] = T-1] of a guitar string depends upon the mass m, the
length l, and tension F. Show that the relationship between them is:
4. A fluid flows at a velocity v through a horizontal pipe of diameter D. An orifice plate containing a hole of
diameter d is placed in the pipe. It is desired to investigate the pressure drop, DP, across the plate.
Assume that
where r is the fluid density. Determine a suitable set of pi terms.
5. In a fuel injection system, small droplets are formed due to the breakup of the liquid jet. Assume the
droplet diameter, d, is a function of the liquid density, r, viscosity, m, and surface tension s ([s] = MT-2),
and the jet velocity, v, and diameter, D. Form an appropriate set of dimensionless parameters using m,
c, and D as repeating variables.
6. Why do we still use more than one system of units?
7. Why are physical phenomena sometimes expressed in terms of dimensionless variables?
8. Name at least 2 examples of distorted models and state which type of similarity was violated.
9. When can we neglect terms in a non-dimensional equation?
10. What would animals look like if they lived on a planet whose gravity were ten times that of earth?