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- Problem 3 The velocity field of a fluid particle is given by the expressions и %3D (Ах + Вy)t v = (Cx + Dy)t while the motion of the fluid particle is described on the table shown. Position (x, y) m (1, 1) (2, 1) v (m/s) -1.0 Time (s) u (m/s) 1.5 0.5 1.0 5.0 -1.0 Determine the acceleration (magnitude and direction) of the particle at t = 1.0 s. Hint: Solve for the constants A, B, C, and D in order to fully describe the velocity field.Consider 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.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 Answer
- QUESTION 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 acerThe 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 IncorrectA 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
- Refer 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) isplease find the flow rate and flow velocity which is represented by Q
- Problem 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+Fr85% @ P 9:25 * ZAIN IQ liı. mechanics 2.pdf Q1: The three forces shown in Figure are required to cause a 250 N as a resultant acting horizontally through point A, determine the values of P. F and T. 1 cm 1 cm B C D