Learning Goal:

To calculate Reynolds numbers, Froude numbers, and Mach numbers.

There are some dimensionless numbers that occur frequently in fluid

mechanics. Three of the most common are the Reynolds number, Froude

number, and Mach number.

The Reynolds number is the ratio of the inertial forces to the viscous

forces in a system. This ratio is expressed as $Re=\frac{VL}{},$ where $$ is

the fluid density, $V$ is a representative velocity, $L$ is a representative

length, and $$ is the dynamic viscosity. The Reynolds number is strongly

related to whether or not a fluid flow is laminar or turbulent.

The Froude number is the square root of the ratio of inertial forces to

gravitational forces. The ratio can be written as $Fr=\frac{V}{\sqrt[\phantom{2}]{gL}},$ where $V$ is

a representative velocity, $L$ is a representative length, and $g$ is the

acceleration due to gravity. This ratio is important in flows with a free

surface. The denominator can also be interpreted as the speed of waves

on the free surface.

The Mach number is the square root of inertial forces to compressibility

forces. The ratio can be expressed as $M=\frac{V}{c},$ where $V$ is a

representative velocity and $c$ is the speed of sound in the fluid. This ratio

gives an indication of how important the effects of compressibility are.

A jet of length $L=20m$ is travelling at $V=450\frac{m}{s}$ at an altitude of $h=7km.$ At that altitude, the speed of sound is $c=312\frac{m}{s},$ the density of air is $=0\mathrm{.}5895k\frac{g}{m^3},$

and the viscosity is $=1\mathrm{.}576{10}^{-2}cP.$ What is the Reynolds number?

Express your answer to three significant figures.

View Available Hint$($s$)$

$Re=$

Part B $-$ Calculate a Mach number

A jet of length $L=10\mathrm{.}8m$ is travelling at $V=555\frac{m}{s}$ at an altitude of $h=6000m.$ At this altitude, the speed of sound is $c=312\frac{m}{s}.$ What is the Mach number?

Express your answer to three significant figures.

View Available Hint$($s$)$

$M=$

Part c $-$ Calculate a Froude number

An $L=50\mathrm{.}6m$ ship is cruising in the ocean at a speed of $14\mathrm{.}5\frac{m}{s}.$ What is the Froude number?

Express your answer to three significant figures.

View Available Hint$($s$)$

$A$

darr

vec

$?$

$Fr=$