1.6 An incompressible Newtonian fluid flows in the z-direction in space between two par- allel plates that are separated by a distance 2B as shown in Figure 1.3(a). The length and the width of each plate are L and W, respectively. The velocity distribution under steady conditions is given by JAP\B² Vz = 2µL a) For the coordinate system shown in Figure 1.3(b), show that the velocity distribution takes the form JAP|B²| Vz = 2µL Problems 11 "L. 2B --– € (a) 2B (b)

Please answer both

i didnt understand 3 fluid mechanics questions. please help me :) i will send of the three part

Fluid Mechanics II Sheet NO (04) Damietta University Faculty of Engineering Mechanical Engineering Dept. FACULTY OF ENGINEERING DAMIETTA UNIVERSIm bluas daola-dunigil us 3- Fluid flow between two horizontal infinite parallel plates with a spacing of H mm shown in figure 3. Determine the volume flow rate per width and the shear stress on upper and lower plates. U2 , draw the velocity profile distribution. U1 Moving plate H Moving plate U2 Figure 3 , a tornado can be approximated As illustrated in Fig. 4 by a free vortex of strength I' for r > Re, where R̟ is the radius of the core. Velocity measurements at points A and B indicate that V = 125 ft/s and V3 = 60 ft/s. Determine the distance from point A to the center of the tornado. Why can the free vortex model not be used to approximate the tornado throughout the flow field (r > 0)? 4- B +100 ft- Figure 4

Which option is the correct one? Please help

P1 A thin layer of water flows down a plate inclined to the horizontal with an angle a = 15° in the shown coordinate system. If the thickness of the water layer is a=0.5 mm, assuming that the flow is laminar and incompressible, (water density p = 1000 kg/m³viscosity µ = 0.001 Pa.s and acceleration of gravity g = 9.81 m/s²) and an air flow shears the layer in a direction opposite to its flow with a shear stress of 1 N /m². Solve the Navier-Stokes equation: air water (a) to find the value of the maximum water velocity in m/s to three decimal points, Answer: (b)and to find the value of water velocity at the layer's surface in m/s to three decimal points, Answer:

Fluid mechanics

Question 2 (Potential flow) a) The velocity component of an incompressible and 2-dimensional flow is given by Determine i. ii. iii. u = -x + 4y v = 2x - y The resultant velocity at point (-1m, 1m) The stream function The velocity potential

a. Given the velocity field u=(u,v,w) in Cartesian coordinates with u=2x+y, v=2zt, w=0. i. Find the equations of the corresponding streamlines (Eulerian concept) ii. Find the equations of the corresponding particle paths, i.e., the pathlines (Lagrangian concept). b. Show that the Vu=0 everywhere implies that volumes are conserved, i.e., the volume of red particles at t-0 is the same as at t=t. Hint: Write out what you must prove and use the theorems to get there.

4. Consider the steady, two-dimensional velocity field given by: u = 2xy-y²; v=x-y². Show that it is a possible 2d incompressible flow. Find the component of acceleration in x direction of a fluid particle at point (x, y) = (1,2)