Fluid Mechanics

REQUEST: files to be submitted on Canvas: 1. PowerPoint Report based on provide template (please do not change anything in the template, just add your image/animation or important analysis onto the slides) 2. Mesh file msh 3. Case file.cas NOTES 4. Please don't work for your friend under any circumstances. 5. You can be asked to submit the workbench zip file wbpz file (File Archive) any time during marking. 6. If you fail to prove you do the work yourself, your case will be transferred to Student Conduct team.

7) Ethanol (u=1.2 x 10-³ Pa*s, p= 788 kg/m³ at 20°C) flows from tank A to tank B via a galvanized iron circular pipe with a diameter of 7.5 cm. The pipeline is 16m long and contains two 90° elbows. Tank A is 2 m higher than tank B. Both tanks are open to the atmosphere. Determine the volumetric flow rate (m³/s) of ethanol.

Question 1 a. Explain with equations what is meant by a partial differential equation (PDE) b. State and briefly explain the types of partial differential equations c. In each of (b) above, give examples or application areas and the properties of each type of PDE. d. Considering the following modified wave equation (i) Show that this wave equation is of the hyperbolic type of PDES. (ii) derive the equivalent system of three first order equations from equation (1) and show that this system is also hyperbolic. (iii) Further considering the related system of equations, determine the characteristic directions and show that there is an extra characteristic equation.

Question 2 a. Use the general technique of converting differential coefficients to algebraic expressions to determine the coefficients a to d in the expansion of the temperature distribution:

Consider the case of a undirectionally flowing fluid between two parallel plates with the top plate

1. A pressurized tank contains oil (s = 0.9) and has a triangular gate of negligible weight, as illustrated below. Compute the magnitude of force F so that the gate remains closed as shown. Note: Since the gate is non-rectangular, you should perform the above problem using the general approach, however you cannot use F = yh₂A nor y₂ = Yc+Ixx.c/Ayc because these equations were derived while taking pressure equal to zero at the liquid surface. Meanwhile in this problem pressure is not equal to zero at the surface of the oil. Thus, looking back at the week 8/part 1 lecture notes posted on Canvas, you should re-derive the expressions for F and y, valid for non-zero pressure at the surface.

Let's write a simple text based game. It is a game in which the main character is avoided by avoiding

Question 1 In the figure below you have two opened tanks. The first one receives a steady flux of water and discharges through a pipe at the bottom into a second tank below. Using the geometrical measures given below, you have to determine the water depth ha

Question 2 The Figure below shows a nozzle through which there is steady flow of water. The outlet of the nozzle is open to the atmosphere. By using the data in the next paragraph, you must determine the horizontal component of force required to keep the nozzle in place. Please, comment on the result.

Question 3 Arectangulargate (shown in the figure below) is located at the end of a rectangular passage that is connected to a lake filled with an unknown liquid. The gate is hinged at the bottom and held closed by a horizontal force FH, applied to the centre of the gate. On the surface of the lake is stationing a river barge whose cross section is approximately rectangular. Its draft (depth of submergence) is hB. Determine the maximum water depth, h, above the centre of the gate that can exist without the gate opening. Is the answer the same if the gate is hinged at the top?