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# Fluid Mechanics I ME 311

CSU Pomona

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This 38 page Class Notes was uploaded by Gerhard Leuschke II on Saturday October 3, 2015. The Class Notes belongs to ME 311 at California State Polytechnic University taught by Maryam Shafahi in Fall. Since its upload, it has received 19 views. For similar materials see /class/218338/me-311-california-state-polytechnic-university in Mechanical Engineering at California State Polytechnic University.

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Date Created: 10/03/15

Fluid Statics ME311 Maryam Shafahi Winter 2011 Pressure Force on Submerged Plane Surface Let us now consider application of pressure force in a different case a surface area is submerged under fluid what will be magnitude and direction of the pressure force Where will the pressure force be acting at Application 439 Consider the car below is partially submerged under water in a flooded street If you are stranded inside the car what force do you need to apply to the car door in order for you to open it Application II A plug is at the bottom of a sink In order to drain the sink what force is required to unplug the plug Application lll You are building a dam What does the dimension of the dam has to be so that it will not topple over What is the maximum depth that is allowed for the reservoir Application IV You are building roadways on a hill side When it is raining hard the soil becomes saturated with water and starts to exhibit characteristics of fluids and the pressure force starts to push on the concrete slab that is protecting the slope How big is the pressure force and will it destroy the slab Road surface I Soil Concrete slab Calculate Pressure Force on Inclined Plane In order to calculate the pressure forces in the above 4 scenarios we will need to figure out how to calculate pressure forces on an inclined plane Let s take a look at the following slide for a figure of a plane that is submerged Centroid c Location of resultant force center of pressure CP Calculate Pressure Force on Inclined Plane The force acting on the differential area dA is a pressure force Thus we can use an integral to define the resultant force FR IpdA 4 Pressure is dependent on depth so we can define P as u Substitute into force equation Calculate Pressure Force on Inclined Plane Define distance from fluids surface to the centroid along the direction of the inclined plane in u I ll 0 I r y Iquot 4 Substitute to force quation Which simply states that the pressure force acting on an inclined plane is directly depended on specific weight of the fluid height from centroid of plane to free surface and the plane area Graphical Representation Let us take a look at the following example WW 4 The picture on the left shows the original pressure distribution on the inclined surface The picture on the right shows that the trapezoidal distribution has been replaced by a single force In order to make the two systems equivalent the single force needs to be applied at a particular location Center of Pressure From Statics we know that in order for two systems to be equivalent the sum of the forces must be equivalent and the sum of the moments needs to be equivalent as well WWW So for the above two systems to be equivalent the singleforce replacement is at a specific point where the moments of the two systems are equivalent as well The point is called center of pressure Center of Pressure If we equate moment about the x axis if A The integral in the numerator is the second moment of the area moment of inertia xc yR yc up Check Fig 218 to find the moments for some geometrical shapes Center of Pressure xc f 39gtyca The point through which the resultant force acts is called the center of pressure Example The inclined surface shown hinged along edge A is 5 m wide Determine the resultant force FR of the water on the inclined surface Net hydrostatic pressure distribution on gate Given Rectangular gate hinged along A w5m Find Resultant force FR We solve this problem by using idirect integration ii the algebraic equations FR 2 IpdA hDysini9 dAle A Integral equations Net hydrostatic aressure dwstr rbution on gate L FRyR wayD ysin 6dy 0 2 3 L sz Dy y sin6 FR 2 3 0 Algebraic Equations FE prA pghCA pgD sin6Lw Maryam Shafahi Winter 2011 ME 113 Fluid Mechanics ME 311 Textbook Fundamentals of Fluid Mechanics Munson Young OkiishiHuebsch Class TuThu 10451200 Instructor Maryam Shafahi Email mshafahicsupomonaedu Office 9 222 Office hours TuThu 9301030 230330 2 midterms 25 each Quiz 10 Final 40 Class activity 5 HW submit them in Bb ME 113 Fluid Mechanicsl Dimensions and units Basic dimensions M L TG Or F L T 9 System of units SI BG EE SI International system kg m s K N m s K BGBritish Gravitational system slug ft 5 R lb ft 5 R EEEnglish Engineering system Ibm ft 5 R lb ft 5 R Newton s second law Fma 1 slug 32174 Ibm ME 113 IFluici Mechanics I Example 12 A tank of liquid having a total mass of 36 kg rests on a support in the equipment bay ofthe space shuttle Find the force in newtons tank exerts on the support shortly after lift off when shuttle is accelerating upward at 15 ftsz 2F ma Ff WzmagtFfmga i l Be careful about the unit system ft03048 m Ff 518 kgms2 518 N The direction is downward since the force shown on the free body diagram in the force of the support on the tank ME 113 Fluid Mechanics l Physical properties Density p mass per unit volume kgm3 slugsft3 Sped cvohnnevyvohuneperunnrnass v1p n kg Specific weighty weight per unit volume V pg N m3 Specific gravity 56 p pHZO4C IdealGasLaun pWRT Viscosity u describes the fluidity of the fluid ifquot du TZIle y t shear stress dimension FtA Newtonian fluid Example This sled slides along on a thin horizontal layer of water between the ice and the runners The horizontal force that the water puts on the runner is equal to 12 lb when the sled s speed is 50 fts the surface area in contact with the water is 008 ft2 and water viscosity is 3510395 lbsft2 Determine the thickness of the water layer under the runners Assume a linear velocity distribution in the water layer Given F A uu FindD FTA 1 39udy 39uD u Fu A D D11710394 ft ME 113 IFluici Mechanics I Viscosity NonNewtonian fluids Bingham plastic Shear thinning fluid the harder sheared the less viscous polymer solution latex paint Shear thinning HNewtonian Shearing stress 7 Shear thickening fluid the harder sheared the more viscous watercorn starch watersand starch Shear thickening Bingham plastic yield stress without motion du Rate of shearing strain dy toothpaste mayonnaise Viscosity is a function of temperature CT32 S and C are empirical constants Sutherland equation T S D and B are constants Andrade s equation a DeBT ME 113 lFluid Mechanics l Compressibility of the fluid Bulk modulus EV dpdvv ME 113 IFlu ci Mechanics I Surface tension Interface of a liquid and a gas or between two immiscible liquids surface behaves like a skin stretched over the fluid mass The intensity of the molecular attaraction per unit length along any line in the surface is called the surface tension 0 ME 113 Fluid Mechanics I Surface tension Pressure inside a drop of liquid 27rR0Ap7rR2 gt Ap 19 pe ZYO Capillary WrRZh 27rR0 cos 6 20 cos 6 yR h wetting Nonwetting VIE 113 Fluid Mechanics I Example Capillary raise in a tube What diameter of clean glass tubing is required so that the rise of water at 20 C in a tube due to capillary action as opposed to pressure in the tube is less than hl0 mm 11 Zacos oSe3 R00149m nk 3911 Fluiillrlerlialwsl Example 39 A layer of water flows down an inclined fixed surface with the velocity profile shown in the figure Determine the magnitude and direction of the shearing stress that the water exerts on the fixed surface for U2ms and h01 m Tdu dy ziy dy h h2 du U Tw 2 dyyZO h tw ME 113 Fluid Mechanicsl Summary Systems and dimensions Specific weight Specific gravity Newtonian fluid shear stress Bulk modulus Capillary rise in a tube Shear stress ME 113 Fluid Mechanics I ME 311 Fluid Statics Forces on Plane Surfaces Maryam Shafahi Mechanical Enginaaring Dapartmant Example 27 of the book Example For a vertical gate shown below if the top of the gate is 4 m below water level determine magnitude and location of the pressure force if the gate is of the following shapes gate ll 5m 5m Find Centroids First You can find information on centroid and moment of inertia from Fig 218 Find Moment of Inertia Next Note semicircle and quartercircle are special cases which we will discuss on a separate slide gate 5m 4 D T AV Em C d 3 3 3 3 3 3 KW jzs 5 In M 25 5 5621 55 Ixc 20054881134 4 E36 5 36 312 Plug in the formulas to get your answers 439 Note In this case since the gates are vertical hC and yC are the same J Case a FzyhcA984130552 54 I E yR yCA yc10 ye 43552 4 Try to calculate for Cases b and c on your own Quarter and Semicircles So for part d in the prior case 45 F7hCA9845 3557Z394 7r 1 00554 gtXlt yRycxj445 i5 45 ye 45 3 557r4 7239 Determine the force P needed to hold thew wide gate in the position shown in Fig

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