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- The Richardson number is defined as Ri =L5g Δρ / ρV .2 Miguel is working on a problem that has a characteristic length scale L, a characteristic velocity V, a characteristic density difference Δ? , a characteristic (average) density ? , and of course the gravitational constant g, which is always available. He wants to define a Richardson number, but does not have a characteristic volume flow rate. Help Miguel define a characteristic volume flow rate based on the parameters available to him, and then define an appropriate Richardson number in terms of the given parameters.A two-dimensional flow field for a liquid is defined by V[(z+2y³)i + (2x-3y)j m/s, where z and y are in meters Part A Determine the magnitude of the velocity of a particle located at (-2 m, 1.2 m) Express your answer to three significant figures and include the appropriate units. V= Submit Part B Request Answer Determine the direction of the velocity of a particle located at (-2 m. 1.2 m). Measure the angle counterclockwise from the positive z axis. Express your answer in degrees to three significant figures. 0- Submit Request AnswerConsider a fully filled tank of semi-circular cross section tank with radius R and width of b into the page, as shown. If the water is pumped out of the tank at flow rate of V· = Kh2, where K is a positive constant and h is the water depth at time t. Determine the time needed to drop the water level to a specified h value of ho in terms of R, K, and ho.
- The velocity field of a fluid v (in meters per second) has divergence div(v)(P) = 3 at the point P = (1, 1, 4). Estimate the flow rate out of the sphere of radius 0.4 centered at P. (Use decimal notation. Give your answer to four decimal places.) flow rate: 2.0106 IncorrectQUESTION 3. Velocity components of a two dimensional fluid flow are: u = 2xy+t and v = x-y + 12t. a) Is the flow physically possible? b) Is the flow a permanent flow (steady-state flow)? c) Is the flow a potential flow? If it is a potential flow, obtain the potential velocity function. d) Determine the stream function. e) For t = 1 s, find the velocity and acceleration components of the flow and these values for the point M (1,1). (35p) Good Luck >> Desktop acerA fluid flow is represented by the velocity field = ax + ay 1, where a is a constant. The equation of streamline passing through a point (1, 2) is (a) x - 2y =0 (b) 2x+y=0 (c) 2x-y=0 (d) x+2y=0
- Given a portion of a water supply pipe network system below. Determine the actual flow in each pipe and the respective head losses. Assume flow in pipes AB and BC in loop Il and I respectively equal to 0.142 m/s clockwise and 0.038 m/s clockwise for the first trial. Use Manning's Equation with n = 0.011. Length (m) 700 800 Diameter (cm) Pipes AB 30 BC 15 CD 1100 25 DE 650 35 EA 300 10 BD 1500 10 Qq = 0.15 m'ls QA = 0.10 m/s Qc = 0.10 m'/s Loop I Loop II E A Q = 0.15 m'/sRefer to Figure 03.24. Given that H, = 300 mm, H2 = 500 mm, and ly - 600 mm and that at z = 200 mm, l1 - 500 mm. It is required to determine li at z = 600 mm. The following general equations may be useful: kre=H/[(H/k1) + (Hz/kız) + ... + (H./k..)] - (1/H) kw H, + ki2 H2 + ... + k H.) a) What is the ratio ki/ky? b) What is the value of h at z = 600 mm? c) If k, = 5 x 106 cm/s, what is the equivalent k of soils 1 and 2? Water supply B Figure 03.24The velocity potential function in a two-dimensional flow field is given by $ = x² - y² 2 Ф y2 X The magnitude of velocity at point P (1, 1) is
- please find the flow rate and flow velocity which is represented by QProblem 1: Derive the following macroscopic models for n = 0 and n ≥ 1 a.) U-k relation b.) U(max) c.) k(max) Problem 2: If the relation between speed (u) and density (k) is given by: -bk u = ae where a and b are constants. (e-natural base logarithm) Determine the maximum flow. Problem 3: A public school holds its flag ceremonies every Monday from 7:00 AM to 7:15 AM. During the singing of the national anthem, which lasts for about 2 minutes, all drivers stop in front of the school as an act of respect. Determine the characteristics of the shock waves formed by this activity. Estimate the time required for the traffic flow to be back to normal.Example 15.5 In a flow through a rectangular channel for a certain discharge the Froude 2/3 numbers corresponding to the two alternate depths are Fr, and Fr,. Show that Solution : Fr₂ Fr₁ 2+ Fr 2+Fr