CHEMENG 2018: PROCESS FLUID MECHANICS TUTORIAL 3 (Due: 28 April 2017) Questions due for assessment:1 A water jet impinges on a plate as shown in Fig....

answer question 3.8.....................................

CHEMENG 2018: PROCESS FLUID MECHANICSTUTORIAL 3(Due: 28 April 2017)Questions due for assessment: 3.2, 3.3, 3.4, 3.6, 3.8, 3.93.1 A water jet impinges on a plate as shown in Fig. 3.1. Find the magnitude of the force F acting onthe plate to keep it stationary.Ans: 106 ND =0.075 m Fig. 3.13.2 Fig. 3.2 An open tank of water is connected to a pipe having a uniform diameter of 75 mm, as shown inFig. 3.2. Assuming the flow through the pipe is steady and frictionless, determine the following:a. Flow rate of water flowing in the pipe in [m3/h].b. The pressures at points A, B and C.c. The magnitude and direction of the force acting on the pipe.State clearly any assumptions made in your calculations.Aprox. Ans: (a) 50 m3/h (b) pA = 24.5 kPa; pB = - 4.9 kPa (c) 108 N in horizontal flow direction 3.3 Find the magnitude and direction of the force required to hold the box in Fig. 3.3 stationary forthe following situations:a. Gravity is perpendicular to the horizontal x-y plane. b. Gravity is in the negative y-direction. The fluid is water at 20oC, and the mass of the box and its content is approximately 1 tonne.Assume that flow is uniform and frictionless, and that pressures at all outlets are atmospheric.Approx. ans: (a) 4.1 kN; - 6.7o from x-axis; (b) 10.2 kN; 67o from x-axis Fig. 3.3 Page 1 of 2 3.4 An object is placed in a horizontal circular pipe through which water flows continuously.Immediately upstream of the object, the pressure is 5.20 kPag and the fluid velocity is uniform at1.2 m/s. The downstream pressure is 4.80 kPag and the downstream velocity is given byv 1.5 1 r 2 R 2 m/s , where R = 0.15 m is the inside radius of the pipe. Find the magnitudeand direction of the force (drag) on the submerged object. Any assumptions used must bestated.Ans: 77 N in flow direction 3.6 The power output, P, of a hydraulic turbine depends on the fluid density (), the height (h) of thewater surface above the turbine, the gravitational acceleration (g), the volume flow rate (Q), theturbine wheel angular velocity (), the turbine efficiency (), and the turbine wheel diameter (D).Develop a dimensionless functional relation for this process.A possible valid answer: P3 5 F Q 3 , g2 , h , D D D D 3.7 The average diameter (d) of droplets formed when a liquid is sprayed from a nozzle depends onthe fluid velocity (v) from the nozzle, the nozzle tip diameter (D), the liquid density () andviscosity (), the surface tension between the liquid and air (), and the gravitationalacceleration (g). Apply the Buckingham dimensional analysis to find appropriate dimensionlessgroups for this process. Identify and name any familiar dimensionless numbers involved. Ans. A possible valid answer: d F Dv , , gD2 D v v 3.8 A process fluid is discharged through a pipe into an open tank. The discharge rate is to bestudied from a 1:25 scale model.a. What must be the ratios of velocity, discharge rate, and kinematic viscosity betweenprototype and model in order to satisfy dynamic similarity requirements? b. Can all of the above requirements be met, and why? c. If the process fluid is an oil (SG = 0.78; viscosity = 100 cP), what would a suitable fluid forthe model be? Justify your answer. Hints: Both viscous and gravity forces are significant in this problem. Develop thedimensionless groups pertinent to the process before answering the questions.(a) 5, 3125, 1253.9 In hydraulic transport of solids by pipeline, when the fluid velocity exceeds a critical value, thesolid particles will rise and be carried by the fluid along the pipe. A model pipeline system is tobe used to study this critical velocity. From experience, the critical velocity (vc) is known to be afunction of the pipe diameter (D), particle diameter (d), the fluid density (), the fluid viscosity(), the density of the solid particles (s), and the gravitational acceleration (g).a. Use the method of dimensional analysis to determine the pertinent dimensionless groupsfor the process.b. The model used is 1/5th in scale as compared to the prototype, and fluid density scale iskept at 1.0. Can all similarity requirements be met with for the model? What should theviscosity ratio be? c. If a test from the model gives a critical velocity of 3.8 m/s, what would the predicted criticalvelocity in the prototype be (assuming all similarity requirements are satisfied)?3 2Ans. (a) A possible valid answer: Dv F d , s , gD (b) m/p = 0.089 (c) 8.5 m/s 2 D Page 2 of 2