The velocity field of a flow is given by V = 28y/(x2 + y2)1/2j - 28x/(x2 + y2)/2j ft/s, where x and y are in feet. Determine (a) the fluid speed at points along the x axis; (b) the fluid speed at points along the y axis. What is the angle between the velocity vector and the x axis (use the range (-180°; 180°]) at points (c) (x, y) = ( 9, 0); (d) (x, y) = ( 9, 9); (e) (x, y) = (0, 9)? (a) Vx = i ft/s. (b) vy= i ft/s. %3D (c) 0 = (d) 0 = i (e) 0 = i

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 03.24

Consider the general form of the Reynolds transport theorem (RTT) given by dBsys / dt = d/dt ∫CV ρb dV +∫CS ρbV-›r·n-› dAwhere V-›r is the velocity of the fluid relative to the control surface. . Let Bsys be the angular momentum H-› = r→ × mV-› of a system of fluid particles, where r → is the moment arm. We know that for a system, conservation of angular momentum is                                                                                   ∑M-›= d / dt   H-›sys                                                                   where Σ M-› is the net moment applied to the system. Use the RTT and the above equation to derive the equation of conservation of angular momentum for a control volume.

1. A two-dimensional flow has a y component of velocity of v=. ideal, determine the x component of the velocity and find the magnitude of the velocity at the point x = 4 m, y = 3 m. The velocity of the flow at the origin is zero. 4y, where y is in meter. If the flow is

1. Find the general solution to the given homogeneous differential equation: b. y-8y' +7y = 0

The water from a fire hose follows a path described by y=4.0+0.4x-0.20x (units are in metres). If v is constant at 5.0 m/s, find the resultant velocity at the point (2.0.4. Find the magnitude of the velocity of the water at the point (2.0,40). The magnitude is approximately 5.4 m/s. (Type an integer or decimal rounded to one decimal place as needed) Find the direction of the velocity of the water at the point (2.0,4.0). Enter an angle 0 such that 0° ≤0<360° The direction is approximately (Round to the nearest whole number as needed. Type N if the answer is undefined.)

fluid mechanics experts please solve with details and give reasons for steps if needed. note that ax is 0.5 and ay is -0.5. no need to part a and c

in a three-dimensional incompressible fluid flow, the velocity components are:

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.

Within few minutes