Physics & Engineering Worksheet Paper Homework help

Physics & Engineering Worksheet Paper Homework help

 
AE 201
Problem Set 5 –Spring 2022
1. (10 pts) Use Matlab to calculate the properties of the ISA. You may choose to do this in
either SI or USC units. Plot the temperature, pressure and density (in appropriate units) as
a function of altitude up to the tropopause. Note: Be sure to attach a copy of your Matlab
code to your homework submission.
2. (10 pts) A manometer containing water (ρ = 1,000 kg m−3) and mercury (SG =13.6) is
connected to a tank containing air at an internal pressure p, the other end being open to
atmospheric pressure patm of 101×103 Pa, as shown in the figure below.
(a) Using hydrostatic principles, derive an expression for the pressure p1 in terms of patm.
(b) Derive a corresponding expression for the pressure in the tank p in terms of p1.
(c) Obtain a final expression relating p to patm.
(d) If h1 = 25 cm, h2 = 50 cm, h3 = 60 cm, and h4 = 40 cm, then determine the internal
pressure p in the tank.
(e) If the temperature of the air in the tank is measured to be 30◦C, determine its corre-
sponding density.
3. (10 pts) Determine the primary (base) dimensions of each of the following variables: (a)
Plane angle; (b) Specific volume; (c) Stress; (d) Force.
4. (10 pts) A Covid-19 aerosol particle has a density ρp and characteristic size Dp. It is carried
along in the air of density ρ and viscosity μ. In still air, the particles slowly settle out under
the action of gravity and reach a terminal settling speed V . It can be assumed that V depends
only on Dp, μ, g, and the density difference (ρp − ρ). Note: Use the Buckingham Π method
and show ALL steps in your analysis.
(a) Write down the functional dependency of V and the other variables in both explicit and
implicit forms.(b) How many base dimensions and Π groupings are involved in this problem?
(c) Write down the dimensions of each of the variables involved.
(d) Form the dimensional matrix for this problem.
(e) Choose Dp, μ and g as the repeating variables, so then proceed to find the Π grouping
involving V .
5. (10 pts) A weir is an obstruction in an open channel water flow, as shown in the figure below.
The volume flow rate ̇Q over the weir depends on acceleration under gravity g, the width
of weir b (into the paper), and the water height H above the weir. (Use the Buckingham Π
method to answer this problem.)
(a) Write out the functional relationship in explicit and implicit form.
(b) How many fundamental (base) dimensions are involved?
(c) Write out the dimensional matrix for this problem.
(d) Determine the non-dimensional Π groupings that govern this problem.
(e) By how much does the volume flow have to increase to double the value of H?