Liquid flowing at high speed in a wide, horizontal open channel under some conditions can undergo a hydraulic jump, as shown. For a suitably chosen control volume, the flows entering and leaving the jump may be considered uniform with hydrostatic pressure distributions (see Example 4.7). Consider a channel of width w, with water flow at D1 = 0:6 m and V1 = 5 m/s. Show that in general,
Want to see the full answer?
Check out a sample textbook solutionChapter 4 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Thinking Like an Engineer: An Active Learning Approach (4th Edition)
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Engineering Mechanics: Statics
Mechanics of Materials (10th Edition)
Automotive Technology: Principles, Diagnosis, and Service (5th Edition)
Manufacturing Engineering & Technology
- 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_forwardWater flows through a venturi as shown in the figure at a flow rate of Q=49.7 L/s. The inlet and throat diameters of the venturi meter are (D = 3.0 cm and d = 2.5 cm) respectively. The height of water column in the manometers L, and L, are 65 and 53 cm respectively. What is the experimental dynamic head at the throat-{section2} (in m)? LI L3 D 2 d (3arrow_forwardThe 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_forward
- The figure shows a channel with width of 2.4 m. The density of the water is 1000 kg/m^3. The flow is steady. At the entrance of the channel, the flow is uniform with velocity V (m/s) while at the exit, the flow has developed the shown velocity profile u(y) = 4y-2y^2 (m/s) and y is in (m). Answer the following questions. A)The mass flow rate in (kg/s) at the entrance ? b)The velocity in (m/s) at the inlet ?arrow_forwardThe pressure loss p in a pipe is related to the flow rate Q by the equation P = KQ^n, where K and n are constants. If K = 190 x 10³determine the value for n when a flow rate of Q = 0.04 m³/s causes a pressure loss of 180 Pascals.arrow_forwardWater flows in a channel with uniform curvature RR. The channel has height h=6mm and width w=215mm (normal to the drawing plane) as shown in Fig Q3. The curved part of the channel has a length of l=100mm in the x-direction. You can assume that the channel height is very small compared to the curvature radius.Neglect effects of gravity. Fig Q3: Geometry of curved channel, drawing not to scale. The curvature of the channel is not shown, as too small to be drawn accurately at this scale. Work to 4 significant digits. Enter all values using base units or their combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa. You can use values with exponents, such as 0.12e3. Determine the velocity in the middle streamtube, if the overall flowrate is to be the same as 46m/s. Determine the pressure gradient in the streamtube in the middle and determine the pressure difference across the streamtube in the middle:arrow_forward
- Water flowing at 1.0 ft/s in a pipe passes into a constriction where area is one-tenth the normal pipe area. What is the decrease in water pressure in the constriction? The weight density of water is 62.4 lbs/ft^3. (Figure, Formula, Solution)arrow_forwardFLUID FLOW Example 5: A liquid food with a density of 800 kg/m³ is being transported at a rate of 5 ton/h through the system shown below. If the pressure at point 1 is 20 kPa gage, determine the pressure at point 2. Neglect friction losses. Example 5 P₁ = 20 kPa D₁ = 0.08 m 6 m 2 FLUID FLOW P₂ = ? D₂ = 0.025 marrow_forwardA pipeline with roughness ks = 1.0mm and diameter D = 8.8cm connects two reservoirs. The reservoirs are both open to the atmosphere and differ in surface elevation by H = 40m. The two reservoirs with the connecting pipe are shown in the figure below. You can assume density of water = 1003kg/m³, dynamic viscosity of water = 0.001Pas and acceleration due to gravity 9.81m/s². Local losses must be considered; assume reasonable values as introduced in the ENGG2500 lectures. Reservoir 1 = Pipe with: D,K, m. H a) What is the friction factor of the pipe for a flow rate of Q =44L/s? Provide your answer to 3 decimal places. The friction factor f = = b) For this case, what is the length of the pipe? Provide your answer to 3 decimal places. The length is L Reservoir 2arrow_forward
- a) Assuming that the pressure is uniform on each of the channel walls, determine the pressure difference between the upper and lower wall that is needed if the required net force on the two walls is 1850 N pointing downward (in the negative y-direction). Use a sign convention that a positive pressure difference or gradient means the pressure at the higher y-position is higher. The value of the pressure difference is Pa. The value of the pressure gradient across the channel is Pa/m. b) Your team agree that, from experience, the average velocity of the fluid is v = 49. Assuming that the velocity is uniform across the channel, and neglecting gravitational effects, determine the curvature R required to generate this force with this flow velocity. Use a sign convention that a positive value indicates that the centre of the radius is above the channel, i.e. the middle of the channel is bent downwards. A negative radius indicates the middle of the channel is bent upwards. The curvature radius…arrow_forwardWater flows in a channel with uniform curvature R. The channel has height h=6mm and width w=215mm (normal to the drawing plane) as shown in Fig Q3. The curved part of the channel has a length of l=100mm in the x-direction. You can assume that the channel height is very small compared to the curvature radius.Neglect effects of gravity. Fig Q3: Geometry of curved channel, drawing not to scale. The curvature of the channel is not shown, as too small to be drawn accurately at this scale. Work to 4 significant digits. Enter all values using base units or their combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa. You can use values with exponents, such as 0.12e3. a) Determine the pressure gradient in the streamtube next to the lower wall in Pa/m and determine the pressure difference across the streamtube next to the lower wall in Pa. b) Determine the overall force for this velocity profile in N.arrow_forwardWater flows in a channel with uniform curvature R. The channel has height h=ℎ=4mm and width w=200mm (normal to the drawing plane) as shown in Fig Q3. The curved part of the channel has a length of l=115mm in the x-direction. You can assume that the channel height is very small compared to the curvature radius.Neglect effects of gravity. Fig Q3: Geometry of curved channel, drawing not to scale. The curvature of the channel is not shown, as too small to be drawn accurately at this scale. Work to 4 significant digits. Enter all values using base units or their combinations, i.e. m, m/s, Pa, N. Do not use multiples as e.g. mm, kPa. You can use values with exponents, such as 0.12e3.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