MECH 1310 Homework #3 – Dimensions & Units-Infer the dimensions from these dimensions and show that the Reynolds number is dimensionless

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Lastname, Firstname
MECH 1310 Homework #3 – Dimensions & Units Due: 9/19/19
Submission Instructions:
1) An electronic submission of this assignment is required.
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– Write your solution on 8.5”x11” paper. No more than one problem/solution per page.
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NOTE: It is an unreasonable amount of work to collect and grade all the homework you should do to
master the material in a typical engineering/science/math course. Starting with this assignment, homework
assignments may include work not collected for grade in addition to work that will be collected for grade.
If a problem statement is followed by a right-justified pair of square brackets enclosing a number,
the assignment will be collected for grade and a correct solution will earn that many points.
If a problem statement is followed by “[NFG]”,
it is recommended that you work on it for your edification.
Do NOT include an NFG problem in your homework submission. If you do, points will be deducted.
1. The Reynolds number is a dimensionless parameter that is very useful in modeling fluid
flows: Re where: velocity, length, (nu) kinematic
= = = ν = VL V L viscosity
ν
Typical SI units for these variables are (m/s) for velocity, (m) for length, and m2/s for
kinematic viscosity. Infer the dimensions from these dimensions and show that the
Reynolds number is dimensionless………………………………………………………………………… [NFG]
2. The force,
F, of the wind blowing against a building is given by
2
D D
1
where: (rho)= density, = velocity, = area, = drag coefficient.
2
F V AC = ρ ρ V A C
Determine the dimensions of the drag coefficient. ……………………………………………………… [5]
3. Express the following quantities in SI units, (N, kg, m, s), using a reasonable number
of digits. (a) 1,230 in (b) 24×10
3 gal (c) 25 slugs (d) 4.360 lbm/ft3 ……… [NFG]
4. The pressure in a car tire is 32.0 lb/in
2. What is the pressure express in Pascals?……….. [NFG]
5. How much power must be provided to propel an automobile moving at a constant speed of
90 mph if the only force acting on the vehicle is an aerodynamic drag force of 120 lb?
Your answer should be expressed in units of horsepower. …………………………………………. [5]
6. A 10 hp motor drives a rope-and-pulley system to lift objects to a rooftop. What is the
maximum mass (lb
m) that this system can lift at a speed of 180 ft per minute? ……………. [5]?

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