Homework 1 Problem 1 Browse te 331 website to answer: Wen you sould use data symbols on a grap. (Hint ceck out lab reports...) Solution 1 Use data symbols to sow data points unless tere is so muc data tat te symbols overlap. If te data symbols overlap it is better to connect te data points wit a line and not sow te data symbols. In tis case it is imperative tat te number of data points or te data interval be included in te figure caption.if a model or teoretical curve is presented, it sould be a smoot curve witout data points. Problem 2 How can a team member quit or be fired? Solution 2 If no resolution is acieved, te cooperating team members may notify te uncooperative member in writing tat e/se is in danger of being fired, sending a copy of te memo to te course instructor. If tere is no subsequent improvement, tey sould notify te individual in writing (copy to teir instructor) tat e/se is no longer wit te team. Te fired student sould meet wit is/er instructor to discuss options. Similarly, students wo are consistently doing all te work for teir team may issue a warning memo (copy to instructor) tat tey will quit unless more cooperation is fortcoming, and a second memo(copy to instructor) if te non-cooperation continues. Te student wo quits sould meet wit is/er instructor to discuss options. Problem 3 Given tat for an isentropic compression or expansion of gases E v kp and sow tat c E v c kr T were is te molecular weigt of te gas and R is te universal gas constant (not te R used in te Munson text!) Solution 3 c E v c kp Substitute kp for bulk modulus of elasticity at constant volumee v kp We need a relationsip between density and pressure. Te ideal gas law contains tis relationsip P nr T Ideal gas law
nm gas Density as a function of moles (ceck tis units!) n P R T Substitute in to te ideal gas law P RT Solve for Pressure/density c kr T Problem 4 Te force F, tat is exerted on a sperical particle moving slowly troug a liquid is given by te equation F 3πµ D were µ is te fluid dynamic viscosity, D is te particle diameter, and is te particle velocity. Sow tat te equation is dimensionally correct. Solution 4 [ F] ML M [ µ ] T 2 [ D] [ L] [ ] LT [ µ D ] ML T 2 Terefore te dimensions are consistent. L T Problem 5 An important dimensionless parameter in fluids problems wit free surfaces were tere is a conversion between potential and kinetic energy is te Froude number. Fr : gl were is a velocity, g is te acceleration due to gravity and L is a lengt. Determine te Froude number for flow in a stream wit te following conditions : average velocity in te stream 0.5 m s L: 1m dept of water in te stream
g 9.807 m s 2 Ten convert eac of tese parameters to Englis units and recalculate te Froude number. Explain te signficance of tese calculations. Solution 5 Fr : Fr 0.16 gl In Englis units 1.64 ft g 32.174 ft s s 2 L 3.281 ft Fr 0.16 Te results are independent of te units wen using a dimensionally correct equation. Problem 6 A compressed air tank contains 8 kg of air at a temperature of 80 C. A pressure gage on te tank reads 300 kpa. Determine te volume of te tank. (Te gage reads gage pressure and te atmosperic pressure is 101 kpa) Solution 6 P n : nr gas T 8 kg 1mol 0.029kg R gas : 8.314 Nm kpa : 1000 Pa mol K T : 273.15K + 80K T 353.15 K n 275.862 mol P : 300kPa + 101 kpa P 401 kpa T : n R gas P 2.02 10 3 L Problem 7 A layer of water at 15 C flows down an inclined fixed surface wit te following velocity profile.
u U 2 z z 2 2 z u U Determine te magnitude and direction of te searing stress tat te water exerts on te fixed surface for U m/s and 10 cm. ℵ Solution 7 z u 2 U U z2 2 τ µ d dz u U: 2 m s : 10cm µ : 1.12 10 3 kg sm d dz u 2 U 2U z 2 evaluate at z0 to get sear at te solid boundary τ 0 : µ 2 U τ 0 0.045 Pa Te water exerts a sear stress on te fixed surface in te direction of te velocity u. τ 0 0.045 Pa Problem 8 Metane (CH 4 ) at 20 C and standard atmosperic pressure of 101.3 kpa is compressed isentropically to a new absolute pressure of 400 kpa. Determine te final density and temperature of te gas. k : 1.31 Specific eat ratio for metane Solution 8 kpa : 1000 Pa P 12 + 4 nr T ideal gas law M metane 1000 kg mol : molecular weigt of metane nm gas definition of density R gas : 8.314472 joule mole K
PM metane R gas T substitute ideal gas law T i : 273.15K + 20K T i 293.15 K P i : 101.3 kpa P f : 400kPa P i M metane i : R gas T i 0.665 kg i m 3 substitute to obtain initial density P i k i P f k f true for isentropic compression 1 k P f f : P i solve for final density i We will calculate final temperature using te ideal gas law T f P f nr gas : but from density definition M metane T f : P f f R gas M metane n f 1.9 kg m 3 T f 133 C Problem 9 Two vertical, parallel, clean glass plates are spaced a distance b apart. If te plates are placed in 20 C water, ow ig will te water rise between te plates due to capillary action? Plot as a function of b over te range 0.5 mm to 5 mm. Surface tension (N/m) 0.080 0.075 0.070 0.065 0.060 0.055 0.050 0 20 40 60 80 100 Temperature (C) Solution 9 σ : 0.072 N : 1000 kg m m 3 b : 0.5mm, 0.6mm.. 5mm Let L be lengt of te plates, be te capillary rise, and b be te distance between te plates. Ten te weigt of te water is W g b L Te force of surface tension acts along bot plates for a total distance of 2L.
F σ : σ 2 L At equilibrium te weigt and te surface tension force balance g b L σ 2 L b ( ) : 2 30 σ gb 20 b ( ) mm 10 0 0 1 2 3 4 5 b mm Make sure te cecker cecks te omework using te omework guidelines.