4. Air flows into a pipe from the region between a circular disk and a cone as shown in Fig. P4.55. The fluid velocity in the gap between the disk and the cone is closely approximated by V = V₁R²/r², where R is the radius of the disk, r is the radial coordinate, and is the fluid velocity at the edge of the disk. Determine the acceleration for r = 0.5 and 2 m if V0 = 5 m/s and R = 2 m. -Pipe sh Disk Cone

Please include ((fbd))

5. A sprinkler rotates around fixed Point C. The nozzle on Arm A has broken off. So, water exits Arm A in the radial direction, relative to the sprinkler at 2 m/s and the radial velocity of the water is increasing at 0.5 m/s². The sprinkler arms are rotating around Point Cat = 6 rad/s, and because the nozzle has broken, it is decelerating with Ö= -1 rad/s². At that moment, what are the radial (vr) and theta (ve) components of velocity of the water exiting the sprinkler at Point A? b. Express the velocity vector in rectangular coordinates, in terms of i and j unit vectors. a. Y X view from the top 0.1 m 8 = 6 rad /s Ö= -1 rad/s² A *w = 2 m/s *w = 0.5 m/s²

4.71 Water enters a 1.5 m wide, 0.3 m deep channel as shown in Fig. P4.71. Across the inlet the water velocity is 1.8 m/s in the center portion of the channel and 0.3 m/s in the remainder of it. Farther downstream the water flows at a uniform 0.6 m/s velocity across the entire channel. The fixed control volume ABCD coincides with the system at time t = 0. Make a sketch to indicate (a) the system at time ! = 0.5 s and (b) the fluid that has entered and exited the control volume in that time period. B. 0.25 m/s 0.6 m 2 m/s 0.3 m 1.5 m 0.6 m/s i 0.6 m ID 0.25 m/s Control surface Figure P4.71

A two dimensional, steady, incompressible and potential flow field of water (ρ=1000 kg/m3) is given with velocity components u and v. If the velocity component, u is given as u=2xy m/s with the magnitude of maximum pressure in the field as 52108 Pa. a) At x=+1 m and y=+2 m point, what is the magnitude of the velocity component v (in m/s)? (Please use 2 decimal digits in your answer) b) At x=+1 m and y=+2 m point, what is the magnitude of dynamic pressure (in Pa)? (Please do not use any decimal digit in your answer) c) At x=+1 m and y=+2 m point, what is the magnitude of static pressure (in Pa)? (Please do not use any decimal digit in your answer)

4.68 The wind blows across a field with an approximate velocity profile as shown in Fig. P4.68. Use Eq. 4.16 with the parameter b equal to the velocity to determine the momentum flowrate across the vertical surface A-B, which is of unit depth into the paper. 10 ft 15 ft/s Figure P4.68 20 ft 2017- S SATIN Har

The flow pattern in bearing lubrication can be illustrated by Fig. P4.83, where a viscous oil (p, µ) is forced into the gap h(x) between a fixed slipper block and a wall moving at velocity U. If the gap is thin, h< L, it can be shown that the pressure and velocity distributions are of the form p = p(x), u = u(y), v = w = 0. Neglecting gravity, reduce the Navier-Stokes rquations .. to a single differential equation for u(y). What are the proper boundary conditions? Integrate and show that 1 dp ( – yh) + U( и 2д dx where h = h(x) may be an arbitrary, slowly varying gap width. ( Oil inlet Fixed slipper block Oil outlet ho h(x) и (у) Moving wall

If anyone can help with this problem I would appreciate it. Thank you! Answers listed in the book are: a) 5, (b) 4.4 m/s, (c) −ρV 22 H2w((1 + cos θ)i + sin θj), (d) magnitude ×1/4

4.17 The torque T necessary to rotate a disc of radius R a distance h from a flat plate depends on the rotational speed w and the fluid viscosity p.. Relate T to the appropriate variables and fluid density, rho.

Please help me with this question with details. i need answer of these questions with explanation.