Concept explainers
A tank contains water (20°C) at an initial depth y0 = 1 m. The tank diameter is D = 250 mm and a tube of diameter d = 3 mm and length L = 4 m is attached to the bottom of the tank. For laminar flow a reasonable model for the water level over time is
Using Euler methods with time steps of 12 min and 6 min:
- (a) Estimate the water depth after 120 min, and compute the errors compared to the exact solution
- (b) Plot the Euler and exact results.
P5.75
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Statics and Mechanics of Materials (5th Edition)
Engineering Mechanics: Statics
Automotive Technology: Principles, Diagnosis, And Service (6th Edition) (halderman Automotive Series)
Manufacturing Engineering & Technology
Engineering Mechanics: Dynamics (14th Edition)
Thinking Like an Engineer: An Active Learning Approach (3rd Edition)
- The pressure distribution on a object cross section is shown (assume width=1m), where flow is from left to right. What is CL (coefficient lif) of this object? The pressure distribution on a object cross section is shown (assume width=D1m), where flow is from left to right. What is C. (coefficient lif) of this object? a = 45° Cp = - 1.0 Cp = + 2.0 Cp = + 1.8 B = 30° C, = - 0.9arrow_forwardA pressurized tank of water is used to create a fountain, as illustrated. Assume that the water's free surface area in the tank is very large relative to the pipe's cross-sectional area, which is circu- lar with diameter d 1.0 cm. The small pipe bend has height = 10.0 cm. At the instant when 0.75 m, H = 2.5 m, and the gauge measures a pressure of Pgauge 20.0 kPa, the water spray reaches a height L above the pipe exit. h = = = Neglecting viscous effects, determine the height of the spray, L.arrow_forward338 B/s O 1: 56% E 3:01 Question: Gasoline is flowing through this 180° pipe bend. The pipe cross-sectional area is 18 in?. Take the pipe weight as 5 Kg. Flow rate is 0.5 liters/s. Pressure at section-1 6 psia, pressure at section-2 is 4 psia. Calculate the anchoring force required to hold this pipe and also show its direction, referenced to proper 2-dimensional a cartesian coordinate system. (2 1arrow_forward
- A potential flow model of flow over a circular cylinder is described by the following velocity potential R² $ = U_cms (0) (r + 47) Find the magnitude of the pressure gradient normal to the cylinder surface, at an angle of 30° from the leading edge. The constants are given as U = 8 m/s and R = 2 m, while the density of the fluid is p = 1000 kg m-³. Give your answer in Pa/m to the nearest integer value.arrow_forwardb Water flows around the vertical two-dimensional bend with circular streamlines and constant velocity as shown in the figure below. If the pressure is 62 kPa at point (1), determine the pressures at points (a) (2) and (b) (3). Assume that the velocity profile is uniform as indicated. = Esc Type here to search L 1 A 30 @ 2 W S 4x F2 # 3 E 4₁ D O $ 4 R F F4 % 5 2m 99+ FS T G A 6 4 m 1 m Y H (3) (2) (1) * F7 & 7 V = 10 m/s U PrtScn FB 8 Home 9 K 9 End F10 ) 0 L 36°F Clear PgUp F11 P PgDn 40 + (1) 7:00 PM 11/21/2022 Del Backsparrow_forwardProblem (3) Find the rate of change of h(t) (mm/s) if water is the fluid at all locations. Use V₁ = 7.1 m/s and Q = 1000 L/min. m₂ = 10 kg/s 4 cm dia. V₁ Answer: 120 cm h(t) 8arrow_forward
- Water flows past a flat plate that has a length L = 5 m and a width w = 2 m, as shown in Figure Q4. The shear stress at the wall is given by Tw= μ du dy. When the flow is laminar the shear stress at the wall is given by the equation: Tw = 0.0644 pU 2 8 x Where p = 1000 kg/m3 is the water density and U∞ = 5 m/s is the velocity of the water. The height of the boundary layer is 5, and can be approximated by 8(x) = 5√ ux pU* The viscosity of water is μ = 1 mPa.s. a) Estimate the drag force on the plate. You may use the expression FD = | TwdA b) When the flow becomes turbulent, we can approximate the velocity gradient at the wall as constant, au ay = A. If the total drag force is 300 N, find A. c) When the fluid is heated to 900C, the density drops slightly and the viscosity decreases a lot, and engineers observe that the equation, Tw = 0.0644pU 2 6 x, becomes less accurate. Explain why this might occur (1-2 sentences). d) In order to visually examine a turbulent boundary layer, engineers…arrow_forwardQuestion 4 du Water flows past a flat plate that has a length L = 5 m and a width w = 2 m, as shown in Figure Q4. The shear stress at the wall is given by Tw = μ- When the flow is laminar the shear stress at the wall is given by the equation: dy Tw = 0.0644 PU² The viscosity of water is μ = 1 mPa.s. 8(x) = 5 - Where p = 1000 kg/m³ is the water density and U.. = 5 m/s is the velocity of the water. The height of the boundary layer is 8, and can be approximated by μx puo X 1arrow_forwardThe 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_forward
- 6arrow_forwardAt t = 0 the tank shown in fig. is full up to top level, write the differential equation for the function of depth with respect to time. Tank 2 m 2 m conical 1 m 1 m cylinder r = 0.05 m Choose T or F F Case 1: y> 1 case 2: y< 1 m boundary condition at t=tm ,y=1 TI(1)2 dy/dt =0 -cd* t *( 0.05)2 * (2gy)1/2 I(y+1)2 dy/dt =o - cd* n *( 0.05)2 * (2gy)1/2arrow_forwardA pipe is horizontal and carries oil that has a viscosity of 0.14 Pa s. The volume flow rate of the oil is 5.3 × 10^-5 m3/s. The length of the pipe is 38 m, and its radius is 0.57 cm. At the output end of the pipe the pressure is atmospheric pressure. What is the absolute pressure at the input end?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