jFx' 0 '&10 lbf & τA % mgSinθ '&10 lbf & µUhA % mgSinθU 'mgSinθ & 10 lbfµ Ah' (0.002 in)(20lbm 32.174)ft/sec2Sin 35o)32.174ftlbmlbf sec2& 10 lbf0.4Nsm20.0209lbf s m2Nsft2(6in)(6in )U ' 0.006645ft2lbf sec in12 inft1.472 lbf ' 0.117ftsec' 1.41insecgxy35degrees10 lbfHour Exam A MEEN 344 Name:________________________Chapters 1-3 Fall 2001 Open Book, Closed Notes, 50 minutes1. (33 pts) The block at the right has amass of 20 lbm. It is the shape of a cubewith dimensions of 6 in x 6 in x 6 in. The gap under the block is 0.002 inchesthick and is filled with SAE 30 weightoil at 20oC. Determine the terminalvelocity of the block.First suspend item on string in air. Tension in stringTair' ρitemgVitemNext dunk item in water. New tension in string.Twater' ρitemgVitem& ρwatergVitemSolve equations simultaneously.Tair& Twater' ρwatergVitemVitem'Tair& TwaterρwatergSubstitue into TairequationTair' ρitemgTair& Twaterρwatergρitem'ρwaterTairTair& Twater2. (33 pts) Your distant relative gives you a large statue the has a gold finish on it. The relativeclaims it is solid gold. You are not sure. How can you measure the density and volume of thestatue? Draw free body diagrams and the equations you would solve.dP '&ρgdz &&&&&6mPgasPdP 'mDz& ρgdzPgas& P '&ρg( D & z ) for water only want Absolute water pressureP ' Pgas% ρg(D & z)dPA '&dydzˆi % dxdyˆkPFR'&mmAPdPA &&&6 FRz'&mmAPdPA@ˆkFRz'&mw0mD0Pgas% ρg(D & x2) dx dy'&w Pgasx % ρg(Dx &x33)D0'&2m 50,000Nm21.225 m % 1000kgm39.81ms2( 1.837 & 0.6124 ) m2' (& 122500 & 24027) N '&146527 N3. (34 pts) The closed container shown below is partially filled with water and has a gas at apressure of 50 kPa absolute in the area above the water. Determine the vertical force exerted bythe water only on the curved portion of the container and its line of action. The containerhas a dimension of 2 meters in the Y direction.x)FRz'&mmAxPdPA@ˆkx)FRz'&mw0mD0x Pgas% ρg(D & x2) dx dy'&w Pgasx22% ρg(Dx22&x44)D0'&2m 50,000Nm20.75 m2% 1000kgm39.81ms2( 0.75 & 1.125 ) m3' (& 75000 % 7357.5) Nm '&67,642.5 Nmx)'&67,642.5 Nm& 146,527 N'0.462 mZXGas at 50 kPa absoluteWater20 oCZ=X21.50mg@PV 'ux%vy%wz'(5x/sec)x%(&5y/sec)y%(0)z@PV ' 5/sec & 5/sec % 0 ' 0 IncompressibleDPVDt'PVt% uPVx% vPVy% wPVz' (xˆi & yˆj )5/sect% 5x/sec (xˆi & yˆj )5/secx& 5y/sec (xˆi & yˆj )5/secy% 0 (xˆi & yˆj )5/secz' 0 % 25x/sec2ˆi % 25y/sec2ˆj % 0 ' xˆi % yˆj 25/sec2Vorticity '  XPV 'ˆiwy&vz&ˆjwx&uz%ˆkvx&uy'ˆi(0)y&(&5y/sec)z&ˆj(0)x&(5x/sec)z%ˆk(&5y/sec)x&(5x/sec)y XPV ' (0 & 0)ˆi & (0 & 0)ˆj % (0 & 0)ˆk ' 0Hour Exam B, 50 minutes MEEN 344 Name:_______________________Chapters 4, 5, and 6 Fall 2001 Open Book, Closed Notes1. (33 pts) The velocity vector for a flow field is given by:PV '5secxˆi & yˆjShow mathematically your answer to the following questions:a) Is the flow incompressible?To determine if the flow is incompressible, evaluate . If this equals zero, the flow is@PVincompressible.b) What is the acceleration of a fluid particle?The acceleration of a fluid particle is given by the substantial derivation of the velocity vector.c) What is the vorticity of the fluid?P1ρ%V212% gz1'P2ρ%V222% gz2z2& z ' 10 m 'P1ρg%V212gP2ρ%V222% gz2'P3ρ%V23ρ% gz3z3& z2' 10 m 'V222gV2' (2)(9.81 m/sec2)(10 m) ' 14 m/sP1' (10 m)(1000 kg/m3)(9.81 m/s2) &12(1000 kg/m3)(7 m/s)2' 98.1kPa & 24.5kPa ' 73.6kPaFsurface&vertical% Fbody&vertical'tmmmCVρVverticald (Vol)mmcontrol&surfac( Vvertical)ρPV@dPARy% P1A1& mg ' 0 % (7 m/s) &(1000 kg/m3)(7 m/s)(0.01 m2)% (14 m/s) (1000kg/m3)(14 m/s)(0.005 m2)Ry'&P1A % mg & 490 N % 980 NRy'&(73600 N/m2)(0.01 m2) % (4 kg)(9.81 m/s2) % 490 NRy'&736 N % 39 N % 490 '&207 N2. (33 pts) A water fountain designed like the one at Rudder Tower shoots water straight upinto the air. The nozzle on the endo of the supply pipe reduces the area of the supply pipe by afactor of two. What pressure must be present in the supply pipe to have the water shoot 10meters straight up? Neglect the length of the nozzle.Apply Bernoulli’s equation from the supply pipe (position 1) where z1=0 m to the top of thewater plume (position 2) where the fluid velocity is zero, P2=0, and z2=10 m.P1 is what we want but we need to know V1 to get the answer. Now apply Bernoulli’s equationfrom the exit of the nozzle (position 3) where P3=0 and z3=0 to position 2.Then using conservation of mass, V1A1=V2A2. Solving for V1=V2A2/A1=V2 /2=7 m/s. Then3. (34 pts) If the nozzle in problem 3 has a mass of 4 kg and the pipe has an area of 100 cm2,determine the force exerted on the end of the pipe by the nozzle being attached to the pipe andbeing held stationary by the pipe.This is the force the pipe exerts on the nozzle in the vertical direction. Therefore the forceexerted on the end of the pipe will be equal and opposite, 207 N in the upwards direction.Hour Exam C MEEN 344 Name:________________________Chapters 7, 8, and 9 Fall 2001 Open Book, Closed Notes50 Minute Exam Period1. (30 pts) You are asked to find a set of dimensionless parameters to organize data from alaboratory experiment in which a tank is drained through an orifice from initial liquid level ho. The time, τ, to drain the tank depends on tank diameter, D, orifice diameter, d, acceleration ofgravity, g, liquid density, ρ, and liquid dynamic viscosity, µ. Using ρ, g, and d as the repeatingvariables, determine the all the possible Π groups.hoτ Dd g ρ µLt LLL/t2M/L3M/LtNumber Π groups = 7 - 3 = 4Π1 = ho1ρagbdc = (L) (MaL-3a)(Lbt-2b)(Lc)M: 0 + a + 0 + 0 = 0 a = 0t: 0 + 0 - 2b + 0 = 0 b = 0L: 1 - 3a + b + c = 0 c = -1Π1 = ho/dΠ2 = τρagbdc = (t) (MaL-3a)(Lbt-2b)(Lc)M: 0 + a + 0 + 0 = 0 a = 0t: 1 + 0 - 2b + 0 = 0 b = ½ L: 0 - 3a + b + c = 0 c = 3a - b = 0 - ½ = - ½ Π2 = τg1/2 d-1/2Π3 = Dρagbdc = (L) (MaL-3a)(Lbt-2b)(Lc)M: 0 + a + 0 + 0 = 0 a = 0t: 0 + 0 - 2b + 0 = 0 b = 0L: 1 - 3a + b + c = 0 c = -1Π3 = D/dΠ4 = µρagbdc = (M/Lt) (MaL-3a)(Lbt-2b)(Lc)M: 1 + a + 0 + 0 = 0 a = -1t: -1 + 0 - 2b + 0 = 0 b = - ½ L: -1 - 3a + b + c = 0 c = 1 + 3a - b = 1 - 3 + ½ = -1 ½ Π4 = µ ρ-1 g-1/2 d-3/22. (35 pts) A spherical tank 0.2 meter in diameter has a scientific recording instrument inside. Itis anchored to the bottom of the ocean and can be released via a radio signal. Determine therequired mass for the sphere and