The Keystone Pipeline in the Chapter 6 opener photo has D = 36 in. and an oil flow rate Q = 590,000 barrels per day (1 barrel = 42 U.S. gallons). Its pressure drop per unit length,
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Fluid Mechanics
- As measured by NASA's Viking landers, the atmosphere of Mars, where g = 3.71 m/s2, is almost entirely carbon dioxide, and the surface pressure averages 700 Pa. The temperature is cold and drops off exponentially: T≈ TO e-Cz, where C 1.3 \times 10-5 m-1 and TO≈ 250 K. For example, at 20, 000 m altitude, T≈ 193 K. (a) Find an analytic formula for the variation of pressure with altitude. (b) Find the altitude where pressure on Mars has dropped to 1 Pascal.arrow_forwardViscosity can be measured by flow through a thin-bore or capillary tube if the flow rate is low. For length L, (small) diameter D« L, pressure drop Ap, and (low) volume flow rate Q, the formula for viscosity is u = D'Ap/(CLQ), where C is a constant. (a) Verify that C is dimensionless. The following data are for water flowing through a 2-mm-diameter tube which is 1 meter long. The pressure drop is held constant at Ap = 5 kPa. T, °C 10.0 40.0 70.0 Q, L/min 0.091 0.179 0.292 (b) Using proper SI units, determine an average value of C by accounting for the variation with temperature of the viscosity of water.arrow_forwardThe laminar pipe flow example of" design a capillary viscometer|. If Q is the volume flow rate, L is the pipe length, and Ap is the pressure drop from entrance to exit, the theory of Chap. 6 yields a formula for viscosity: can be used to 8LQ Pipe end effects are neglected [29]. Suppose our capillary has r, = 2 mm andL = 25 cm. The following flow rate and pressure drop data are obtained for a certain fluid: Q. m'h 0.72 0.36 1.08 1.44 1.80 Ap, kPa 159 318 477 1274 1851 What is the viscosity of the fluid? Note: Only the first three points give the proper viscosity. What is peculiar about the last two points, which were measured accurately?arrow_forward
- As measured by NASA’s Viking landers, the atmosphereof Mars, where g ≈ 3.71 m/s 2 , is almost entirely carbondioxide, and the surface pressure averages 700 Pa. The temperatureis cold and drops off exponentially: T ≈ T o e - Cz ,where C = 1.3E-5 m - 1 and T o = 250 K. For example,at 20,000 m altitude, T ≈ 193 K. ( a ) Find an analyticformula for the variation of pressure with altitude.( b ) Find the altitude where pressure on Mars has droppedto 1 pascal.arrow_forwardA football, meant to be thrown at 60 mi/h in sea-level air( ρ = 1.22 kg/m 3 , μ = 1.78 E-5 N ? s/m 2 ), is to be testedusing a one-quarter scale model in a water tunnel ( ρ =998 kg/m 3 , μ =0.0010 N . s/m 2 ). For dynamic similarity,what is the proper model water velocity?( a ) 7.5 mi/h, ( b ) 15.0 mi/h, ( c ) 15.6 mi/h,( d ) 16.5 mi/h, ( e ) 30 mi/harrow_forwardWater is flowing at 0.075 cu.m./sec through a glazed porcelain pipe 400m long and 200mm diameter. The pipe roughness is 0.0015mm. Properties of water: Density: 1,000 g/cu.m., viscosity = 0.001 N-m/sec. What is the velocity of water in the pipe? What is the Reynold's number? Steady State flow exists in pipe that undergoes a gradual expansion from a diameter of 6in. Assuming constant density and the inlet flow velocity is 22.4 ft/sec. What is the size of the exit pipe if the exist flow velocity is 12.6 ft/sec?arrow_forward
- Q.5 A plate 1 mm distance from a fixed plate, is moving at 500 mm/s by a force induces a 2 shear stress of 0.3 kg(f)/m. The kinematic viscosity of the fluid (mass density 1000 kg/ 3. m) flowing between two plates (in Stokes) isarrow_forwardAt low velocities (laminar flow), the volume flow Q through a small-bore tube is a function only of the tube radius R, the fluid viscosity u, and the pressure drop per unit tube length dp/dx. Using the pi theorem, find an appropriate dimensionless relationship.arrow_forwardThe pressure drop (Ap) test is carried out using a pipe configuration as illustrated below: Manometer 1 Manometer 2 straight pipe D= 2R R= radius in pipe The pipe data and the flowing fluid are as follows: Pipe: D = 1 cm; L= 100 cm. Fluid: Water, with density (A) = 1000 kg/m"; absolute viscosity (u) = 0.001 kg/im.s); Experimental data is shown as shown in the following table: Task: Ja. Plot the graph of the pressure as a function of the average velocity (V.v). b. Based on the equation for laminar flow in the pipe as follows: Ap = 32VuL, Vavg (m/s) Ap (Pa) 0,001 0,002 0,005 0,01 0,02 0,04 0,06 0,08 0,1 0,12 0,15 0,30 0,62 1,61 3,10 6,10 12,10 20,10 26,00 32,50 38,90 47,20 D Compare the experimental results in the table with the results of calculations using the above equation. Leave a comment. Note: Ap = p1-p2. c. The coefficient of friction (f) in the pipe is formulated as follows: f- 2DAD PL(V.) plot (plot) this distribution of fas a function of the Reynolds number (Re). Re is…arrow_forward
- At low velocities (laminar flow), the volume flow Q through a small-bore tube is a function only of the tube radius R, the fluid viscosity ?܇, and the pressure drop per unit tube length dp/dx. Using the Buckingham pi theorem, find an appropriate dimensionless relationship. Make use of Table 1arrow_forwardAn incompressible fluid flows in a linear porous medium with the following properties: Lenth = 3000 ft k = 100 md p1 = 2000 psig p2 = 1980 psig height = 25 ft porosity = 20% width = 300 ft viscosity = 2 cP Assume the dimension is slanted, i.e., a dip angle of 5 degrees (downward from p1 location to p2 location), what is the apparent fluid velocity under this new boundary condition?arrow_forward(e) An airplane flies at 800km/h at 11700m standard altitude where the ambient pressure and temperature are 20.335 kPA and 216.66K respectively. A 1/50 scale model of the airplane is tested in a wind tunnel where the temperature is 288K. Calculate the tunnel test section wind speed and pressure such that force coefficients of the model and prototype are the same. Assume viscosity is proportional to the square root of T. [ Hint: flow is viscous and compressible; equation of state for a perfect gas applies]arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY