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- In the orifice and Jet flow experiment, the following data were collected: Water level = 30 cm , Volume V {V} L was collected in time 32 seconds, orifice diameter = 6 mm, X1 = 50 mm , X2 = 100 mm, X3 = 150 mm, X4 = 200 mm, X5 = 250 mm Y1 = 3 mm, Y2 = 10 mm, Y3 = 22 mm, Y4 = 38 mm, Y5 = 63 mm What is the actual velocity of water jet that leaves the orifice (m/s)?ME360L Fluid Mechanics Lab Lab #2: Analysis of Bernoulli's Equation for Fluid Flow through Venturi SERIES This accessory illustrates the circumstances to which Bernoulli's Theorem may be applied. It also explains why in other circumstances the theorem gives an inadequate description of the fluid behaviour. F1-15: Manometer bank (e rereR APPARATU EGL H&L Woter td, > dz dz da dg df 31 Bernoulli's Equation, P/y + V/2g+z=CThe slope of the height h of a surface wave moving in a shallow pool of liquid is related to the speed of the wave u and gravity g by the following equation и ди дх g əx (a) Use a length scale L and a velocity scale Vo to 'nondimensionalize' the equation (b) What is the nondimensional parameter of the flow?
- Dimensional Analysis and Hydraulic Similitude (fluid mechanics) 1. Water at 60F at 12 ft/s in a 6-in. pipe. (a) For dynamic similarity, determine the velocity of medium fuel oil at 90F flowing in a 12-in. pipe. (b) Determine the diameter of the pipe that should be used if a medium lubricating oil at 70oF if flowing at a velocity of 50 ft/s. find the: a. velocity : ____________________ fps b. diameter : ____________________ in.Water flows without viscous effects from the nozzle, as shown in Figure Q2 (b). The pressure meter shows a reading of 8X.X kPa (gauge/gage), where "XX" is the last 2 digits of your index number (e.g., If XX is 01, then the pressure is 80.1 kPa) and the water jet is exposed to atmospheric pressure. (b) XX-78 (3) Water jet (2) 0.05 m- 0.8 m •(1)L - 8X.X КРа Figure Q2 (b) (i) Determine the flow rate at the nozzle exit and the height, h if viscous effects are negligible and the specific weight of water is 9.8 kN/m². (ii) Based on your working from Q2(b)(i), explain how the pressure at point (1) and water velocity at point (2) should be adjusted to increase the flow rate at the nozzle exit.1. Answer the following questions: (a) What is the physical meaning of the following: D a +V.v at Dt where V is the velocity vector of the flow field. (b) Let the viscous stress tensor be denoted by 7. How is the surface (vector) force f, acting by the fluid on a surface element ds (with unit normal în ) computed? Give your answer in vector notation and also in index notation. What is the physical meaning of Ty ? (c) Write down the work done on a material volume of fluid by the viscous surface force in vector notation and also in index notation. (d) Write down the amount of conduction heat flux 'q' (a scalar) on a surface element ds (with unit normal în ) in vector notation and also in index notation.
- The Reynolds transport theorem (RTT) is discussed in Chap. 4 of your textbook. For the general case of a moving and/or deforming control volume, we write the RTT as follows: d pb dV + pbV-ñ dA dt dt dB sys where Vr is the relative velocity, i.e., the velocity of the fluid relative to the control surface. Write the primary dimensions of each additive term in the equation and verify that the equation is dimensionally homogeneous. Show all your work. (Hint: Since B can be any property of the flow-scalar, vector, or even tensor—it can have a variety of dimensions. So, just let the dimensions of B be those of B itself, {B}. Also, b is defined as B per unit mass.)(b) One form of fluid movement is rotation and deform angularly. Figure Q1(b) shows the rotation and angular deformation caused by velocity variation about z-axis. Based on Table 1 and setting given to you, derive an equation of rotation. ди Sy St ây > B' ĉu B B ôy dy A' ↑ Sa v+. ôx A ôx Figure Q1(b) : Rotation and Angular Deformation Table 1: Axis of Rotation Setting Axis of Rotation 2 у-ахisProblems H.pdf > Problems H.W: Lecture No.6 Part 2 Q1-(2.4-4, Holland): A fluid of density (p) and dynamic viscosity (u) flows in s.s in a cylindrical pipe of inside diameter (d) with mean linear velocity (u). Derive an expression for the pressure gradient AP/L in terms of p, u, d & u. By dimensional analysis (Note Lect. No.3). Q2-An oil with a viscosity of u= 0.40 N-s/m and density p= 900 kg/m flows in a pipe of diameter d= 0.20m. (a) What pressure drop, pl-p2, is needed to produce a flowrate of Q=2.0x10-5 m/s if the pipe is horizontal with xl=0 and x2=10 m? (b) How steep a hill, part (a), but with pl=p2? (c) For the conditions of part (b), if pl=200 kPa, what is the pressure at section, x3=5 m, where x is measured along the pipe? „must the pipe be on if the oil is to flow through the pipe at the same rate as in II
- Q1: Apply appropriate solution method using math principles to prove that "the pressure at a point in a fluid has the same magnitude in all directions". Support your answer with sketch. Answer: Px Pz = Pn P are the mean pressures at the three surfaces in the x- and z-directions. Q2: Formulate the issue and identify key variables to prove that [AP = P2 - P, = pg Az = y, Az], where y, and p are the specific weight and density of the fluid, respectively. Az is the vertical distance. Support your answer with sketch. Q3: From fluid mechanics science perspective, define the center of gravity and the center of pressure. Q4: Identify the hydrostatic force acting on the top surface of a submerged rectangular plate by applying principles of engineering for the following cases: 1 tilted plate, (2 vertical plate, and 3 horizontal plate. Support your answer with sketch. Q5: By applying principles of fluid mechanics science, define the "rigid-body" and identify its features. Q6: Formulate the issue…Home Work (steady continuity equation at a point for incompressible fluid flow: 1- The x component of velocity in a steady, incompressible flow field in the xy plane is u= (A /x), where A-2m s, and x is measured in meters. Find the simplest y component of velocity for this flow field. 2- The velocity components for an incompressible steady flow field are u= (A x* +z) and v=B (xy + yz). Determine the z component of velocity for steady flow. 3- The x component of velocity for a flow field is given as u = Ax²y2 where A = 0.3 ms and x and y are in meters. Determine the y component of velocity for a steady incompressible flow. Assume incompressible steady two dimension flowSuppose you have crude oil flows through an annulus between two horizontal pipes with the same center, if the velocity distribution, and the average velocity Vavp are expressed by: R R In (R₂/R.) (F)] In- 4μl. R-R ΔΡ SµL R+R In(R./R) Where AP: is the pressure drop through the annulus, u: is the fluid viscosity, L: is the pipe length, R, and R₂: are the inside radius of inner and outer pipes, respectively. Write a program in a script file that calculates the velocity distribution and the average velocity. When the script file is executed, it requests the user to input AP. u. L. R, and R₂ where r has many values between R₁ and R₂. The program displays the inputted values and the calculated average velocity (using fprintf) followed by a table with the values r in the first column and the corresponding values of the velocity distribution in the second column.