Q2. 25 marks A viscous fluid of constant density p and dynamic viscosity u falls due...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Q2. 25 marks A viscous fluid of constant density p and dynamic viscosity u falls due to gravity between two plates a distance 2h apart, as shown in Fig.2. The flow is fully developed, with a single velocity component w=w(x). There are no applied pressure gradients, and gravity is the only body force. (a) Given the Navier-Stokes equation in the vertical direction Hawa² 2²₁ + aw aw 1 + a² w ) + f₂₁ + at ax ay 1 ap az paz plax² ay² az² where (u, v, w) is the flow velocity and (fx,fy, fz) is the body force along the (x, y, z) directions respectively, explain how, after applying the information given to each term separately, it can be reduced to the equation + u aw + V aw + W на2w pax² [4 marks] (b) Integrate the derived differential equation, and write the general solution. [6 marks] + g = 0. (c) State the boundary conditions of the derived differential equation, and explain their physical meaning. [2 marks] (d) Apply the boundary conditions to find one of the integration constants. [6 marks] (e) Apply the boundary conditions to find the other integration constant. [6 marks] (f) Write the particular solution that corresponds to the boundary conditions. h Z, W h X [1 mark] Figure 2: Viscous liquid falls due to gravity between two plates a distance 2h apart. Q2. 25 marks A viscous fluid of constant density p and dynamic viscosity u falls due to gravity between two plates a distance 2h apart, as shown in Fig.2. The flow is fully developed, with a single velocity component w=w(x). There are no applied pressure gradients, and gravity is the only body force. (a) Given the Navier-Stokes equation in the vertical direction Hawa² 2²₁ + aw aw 1 + a² w ) + f₂₁ + at ax ay 1 ap az paz plax² ay² az² where (u, v, w) is the flow velocity and (fx,fy, fz) is the body force along the (x, y, z) directions respectively, explain how, after applying the information given to each term separately, it can be reduced to the equation + u aw + V aw + W на2w pax² [4 marks] (b) Integrate the derived differential equation, and write the general solution. [6 marks] + g = 0. (c) State the boundary conditions of the derived differential equation, and explain their physical meaning. [2 marks] (d) Apply the boundary conditions to find one of the integration constants. [6 marks] (e) Apply the boundary conditions to find the other integration constant. [6 marks] (f) Write the particular solution that corresponds to the boundary conditions. h Z, W h X [1 mark] Figure 2: Viscous liquid falls due to gravity between two plates a distance 2h apart.
Expert Answer:
Related Book For
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala
Posted Date:
Students also viewed these physics questions
-
A viscous liquid of constant density and viscosity falls due to gravity between two parallel plates a distance 2h apart, as in the figure. The flow is fully developed, that is, w = w(x) only. There...
-
A solid cylinder of diameter D, length L, density s falls due to gravity inside a tube of diameter Do. The clearance, (Do D) < < D, is filled with a film of viscous fluid (,). Derive a formula for...
-
A straight and non-moving linear vortex of the initial circulation T, is submerged into a viscous fluid of viscosity u and density p, thus kinematic viscosity of v (think about a straight tornado...
-
Coronado Industries has adopted the following production budget for the first 4 months of 2022. Each unit requires 4 pounds of raw materials costing $6 per pound. On December 31, 2021, the ending raw...
-
West Coast Real Estate Management is expanding operations, and the firms president, Mike Mayberry, is trying to make a decision about new office space. The following are the firms options: Maple...
-
A hospital pharmacy dispensed DrugX to an inpatient pursuant to a medication order. A MedGuide is available for DrugX. When the nurse administered the drug to the patient, the patient asked if there...
-
What are the main components of capital budgeting? What are the three main types of cash flows?
-
Full Throttle Sporting Goods Co. operates two divisionsthe Winter Sports Division and the Summer Sports Division. The following income and expense accounts were provided from the trial balance as of...
-
an determine whether the = 1 are Do hot calculate the limit of converging Sequences Given the following terms corresponding sequences {anban - converging / diverging - - monotone (increasing /...
-
A 2.500-g sample of a mixture of sodium hydrogen carbonate and potassium chloride is dissolved in 25.00 mL of 0.437 M H2SO4. Some acid remains after treatment of the sample. a. Write both the net...
-
Let f(x) = -x / 2. If the graph of f(x) is translated 2 units up and 3 units left and the resulting graph is that of g(x), then g(1/2) =
-
What are OOA and OOD?
-
Which tasks are involved in the OOA process?
-
Write down the purposes of interaction diagrams.
-
What is a found message? What does it mean?
-
Differentiate the purposes of do/action and exit/action in a state notation of a state chart.
-
Problem 2: A 30-tooth pinion drives a 128-tooth gear. Given a diametral pitch of 16 and a pressure angle of 25, find the contact ratio. How does this ratio compare to the recommended contact ratio?...
-
-4 1 9. Let A = Find A-1, (A") and verify that (A")= (A-1)".
-
The two concentric spheres of diameters D i = 20 cm and D o = 30 cm are separated by air at 1 atm pressure. The surface temperatures of the two spheres enclosing the air are T i = 320 K and T o = 280...
-
Oxy-fuel combustion power plants use pulverized coal particles as fuel to burn in a pure oxygen environment to generate electricity. Before entering the furnace, pulverized spherical coal particles...
-
Water enters a hydraulic turbine through a 30-cmdiameter pipe at a rate of 0.6 m 3 /s and exits through a 25-cmdiameter pipe. The pressure drop in the turbine is measured by a mercury manometer to be...
-
The pressure, temperature, and velocity at a certain point in the airflow are 101,325 Pa, 46.85 C, and 1000 m/s. Calculate the total temperature and total pressure at that point.
-
Assuming that a Boeing 747 is flying at a standard altitude of 10,972 m, the pressure at a certain point on the wing is 19152 Pa. Assuming that there is an isentropic flow on the wing, calculate the...
-
The temperature and pressure at the stagnation point of the high-speed missile are 245 C and 790,335 Pa, respectively. Calculate the density at this location.
Study smarter with the SolutionInn App