MECH 314 Midterm, Fall 2017

Fall 2017 Dr. Oweis American University of Beirut Department of Mechanical Engineering MECH 314 - Fluid Mechanics Quiz 1 4 October 2017 1) 5% (Final answer) dw _ Loy O You use a spring-hook weighing scale as shown and measure your own weight when you are fully submerged in a freshwater pool to be 3 kg. Estimating your body volume to be roughly 0.1 m3, what is your average bodily density? Sx DK + oO, |» aN - 0. |/% Se NL r, vy @ So 2 WWF Liq 4sG °. | : (Jo ken? CIRCLE ANY PART ON THE FORMULA SHEET YOU USE IN YOUR SOLUTION 2) 5% (Final Answer & units) The block of weight W is a cube of side length 15 cm and slides down an inclined surface (8 = 30°) at constant speed. There is a liquid film of thickness (h = 0.05 mm) and dynamic viscosity (u = 0.25 Pa.sec) between the surface and the sliding block. The shear stress within the liquid film is constant everywhere and equal to T= “ne is the sliding velocity (V) in mm/sec if the weight (W=7 N). . = L Liquid film of TA = oO wdd~ V di (0 (5) =my SA 8 thickness A <a HON g 7 = + SA V6 ‘ Oe Block contact ; 9 area A ie Oyo V= 3| , (mm/sec) 2/6 3) 10% (Final answer & units) In our class demo on atmospheric pressure we dipped an inverted a water bottle into a cup as shown in the figure. If the water height H = 28 cm, its density is 1000 kg/m, then what is the pressure Px at the top of the bottle? Fill in the blanks below for the pressure Px as absolute, gage, and vacuum. n your answers below make sure to write the correct units. Do not substitute a numerical value for Patm, and just leave it as Patm. Py = Tor “Shy H (absolute) Pit, es Q} Y al ys Peo dF { 4 Te (gage) 2? Py=_—t ot 4 Y NN (vacuum) a 3/6 Mo ad J Ze t put Gate AB is cylindrical in shape of diameter (D = 3.8 m) and weighs 200 kg. It is used to hold the water in|the reservoir to the left. It is pinned at point (A) and is held in place by the external horizontal force (F) as shown. The gate is free to move at point (B) with no friction. If the height of the water in the reservoir (H = 10.4 m), what is the magnitude of the force (F) required to keep the gate in place. It is useful to know that the width of the gate into the page (W = 1.75 m). Neglect the effect of the atmospheric pressure in your computation because it acts on both side of the gate. You are free to solve this problem using the method of your choice. EMy 20 Shh Cuuld E - u(Qx Dep) +f L . tia -~- FD aa ee | \} Fy Fu 4 A = 9.8 410 x pn awk 29.Wib [goa -- +, VW KW «pnb wpwarde. Sul: 553,95 o( 9 xorya 97-0500, Wwe) = F aie 4 > BEEN Ssyg bp aii The stratosphere extends from the surface of the earth (h = 0 km) to roughly an altitude of (h = 14 km), where the atmospheric pressure is known to be #0 kPa approximately. Let the temperature distribution in degrees Celsius in the ix stratosphere vary linearly as (T = 15 — 5h) with (h) measured in km. Starting with an elemental control volume of atmospheric air, derive a formula for the pressure distribution in the stratosphere region, then compute the pressure at the surface of the earth. Hint: you may assume that the atmospheric air is an ideal gas with universal gas constant (R = 287]/kg.K). Also, T(Kelvin) = T(Celsius) + 273. 2 hy, fees Ang ie Raw, WY