Concept explainers
For fully developed laminar flow through a parallel-plate channel, the x-momentum equation has the form
The purpose of this problem is (o develop expressionsfor the velocity distribution and pressure gradient analogous to those for the circular tube in Section 8. I.
(a) Show that the velocity profile,
where
and
(b) Write an expression defining the friction factor, f, using the hydraulic diameter
(c) The friction factor is estimated from the expression
(d) Airflow in a parallel-plate channel with a separation of 5 mm and a length of 200 mm experiences a pressure drop of
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
Fundamentals of Heat and Mass Transfer
Additional Engineering Textbook Solutions
Fundamentals Of Thermodynamics
DeGarmo's Materials and Processes in Manufacturing
Heating Ventilating and Air Conditioning: Analysis and Design
Introduction To Finite Element Analysis And Design
Mechanics of Materials (10th Edition)
Applied Statics and Strength of Materials (6th Edition)
- A capillary tube has an 8mm inside diameter through which liquid fluorine refrigerant R-11 flows at a rate of 0.03 cm3/s. The tube isto be used as a throttling device in an air conditioning unit. A model of this flow is constructed by using a pipe of 3cm inside diameter and water as the fluid medium. (Density of R-11 = 1.494 g/cm3 and its viscosity is 4.2 x10-4 Pa.s; Density of water is 1g/cm3 and its viscosity 8.9 x10-4 Pa.s)a) What is the required velocity in the model for dynamic similarity? Hint: For flow through a tube the Ne number can be expressed in terms of the Reynolds numberb) When dynamic similarity is achieved the pressure drop is measured at 50 Pa. What is the corresponding pressure drop in the capillary tube?Hint: In this case the Euler number defines dynamic similarity with reference to the static pressure droparrow_forward(1) Given the working form of the Bernoulli equation as dW - F dm Where 5 is the friction heating per unit mass dQ F = Au dm Given also that friction heating in laminar flow of Newtonian fluids in circular pipes is given as -AP F = = -gAz = Q Ax u 128 Ax is change in the x-direction. A typical capillary viscometer has a large-diameter reservoir and a long, small diameter, vertical tube. The sample is placed in the reservoir and the flow rate due to gravity is measured. The tube is 0.1 m long and has a 1 mm ID. The height of the fluid in the reservoir above the inlet to the tube is 0.02 m. The fluid being tested has a density of 1050 kg / m. The flow rate is 10* m³ / s. What is the viscosity of the fluid? Typical capillary viscometerarrow_forwardDerive the Continuity Equation by considering a stream-tube of flow through a conduit.arrow_forward
- Q.2 The velocity profile of a fully developed laminar flow in a straight circular pipe, as shown in the figure, is given by the expression R? (dp 1- 4µ ( dx .2 u(r) = %3D R? dp is a constant dx where The average velocity of fluid in the pipe is u(r) R? (dp (b) 4µ ( dx R? (dp (e) - 8µ ( dx R? (dp R? (dp (d) (c) 2µ ( dx, H (dx 응증arrow_forwardQ4) Water at 10°C flows from a large reservoir to a smaller one through a 5-cm-diameter cast iron piping system, as shown in Fig. Determine the clevation z, for a flow rate of 6 L/s. Note that Properties The density and dynamic viscosity of water at 10 e are p= 999.7 kg/m and p- 1.307 x10 kg/m s. Sharp-edged entrance, K = 05 Standard elbow, flanged K = 03 D-5 cm Gale valve. fully open K= 02- Control volume boundary CS CarnscamI TET s Exit. K - 1.06arrow_forwardThe velocity of the mercury at T_∞=250 o C is U_∞=0.033m/sec, and it flows over the pipe bundle of D= 1.25 cm diameter and L=1.2m length. The ratio of the vertical and diagonal spacing distances for the pipes in the shifted plate arrangement is ST /D=SD /D= 1.405. It consists of a matrix with the number of pipe rows in the horizontal direction NL=60 and the number of pipe rows in the vertical direction NT=30. Pipe wall (surface) temperatures are kept at a uniform temperature of T_w=160 o C. Accordingly, find the average heat transfer coefficient, the total heat transfer coefficient from the mercury to the pipe bundle. (Variables: ST /D=SD /D= 0.75-1.975, U=0.02-0.07m/s, L=0.5-1.4m)arrow_forward
- (a) The head loss in 60 meter of 15 cm diameter pipe is known to be 8 meter when oil (s=0.90) of viscosity 0.04 N.s/m? flows at 0.06 m³/s. Determine the centerline velocity, the shear stress at the wall of the pipe and the velocity at 5 cm from the centerline.arrow_forwardThe flow rate of water in a garden hose is measured using the bucket-andstopwatch method. Filling a 5-L bucket takes 75 seconds. If the inner diameter of the hose is 10 mm and the density and viscosity of water are approximately 998 kg m-3 and 0.9 cP, respectively, (a) is the flow inside the hose laminar or turbulent? (b) If the flow rate is adjusted such that the flow is with Re = 2100, how long would it take to fill the same bucket?arrow_forwardA viscous incompressible Newtonian fluid is contained between two fixed parallel plates inclined at an angle 0, and the flow is driven by both constant pressure gradient E = constant) and gravity. The distance between the two plates is 2H and the chosen system of coordinates is shown in the figure. Assuming steady, 2D, and parallel flow (v = w = 0) and using differential analysis: (a) Show that the flow is fully developed using continuity equation; and (b) Find the velocity profile u(y) in terms of ,H,P,g,0,H de using Navier-Stokes equations with appropriate boundary conditions. 211arrow_forward
- The velocity distribution in a 0.02 m diameter horizontal pipe conveying carbon tetrachloride (specific gravity = 1.59, absolute viscosity = 9.6 x 10-6 Pa sec) is given by the parabolic equation: v(r)=0.01(0.12- r?), where v(r) is the velocity in (m/s) at a distance r in (m) from the pipe center. What is discharge? O a. 3.13 x-8 m3/s O b. None of the mentioned O c. 1.047 x 108 m3/sec O d. 4.97 x 109 m3/secarrow_forwardThe head loss for a certain circular pipe is given by hL = 0.0826fL(V.2/D5), where f is the friction factor (dimensionless), L is the pipe length, V. is the volumetric flow rate, and D is the pipe diameter. Determine if the 0.0826 is a dimensional or dimensionless constant. Is this equation dimen sionally homogeneous as it stands?arrow_forwardA horizontal smooth pipe of diameter 5 cm and length 10 m is conducting water ( viscosity= 1x10^-6 m2/s ,density =1000 kg/m3 ) for the presence of laminar flow regime at maximum amount of flow rate determine maximum shear stress magnitude and its position in pipe.ANSWER: 7,36 X 10-3 Pa at wall of the pipearrow_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