Liquid: p, u R. R; Rotating inner cylinder Stationary outer cylinder
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An incompressible Newtonian liquid is confined between two concentric circular cylinders of infinite length— a solid inner cylinder of radius Ri and a hollow, outer cylinder of radius Ro. inner cylinder rotate at
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- Let v(x, y, z) = (-2z, 0, z) represent a velocity field (with units of meters per second) of a fluid with constant density 4 kg/m³. Let S be the surface of the paraboloid z = a? + y? outward. Find the mass flow rate of the fluid across S. Do not include the unit kg/sec/m2 in the answer. 4 with z < 0 such that S is orientedFor an incompressible fluid flow, velocity field and x and z components of velocity are given below. Derive the y-component of velocity. V(x,y,z) = u(x,y,z)i+v(x,y,z)j+w(x,y,z)k u(x,y,z) = –xy² + 2xz и w(x,y,z) = xy+y+3zProblem 1: As shown in Fig. 1(a), a flat-plate airfoil with a chord length c has an angle of attack, a.. Surface pressures on the lower and upper surfaces are p1 and p2, respectively. Calculate the lift and drag of the flat-plate airfoil. Note: Decompose pressure vectors into the vertical and horizontal components that contribute to the lift and drag, respectively. Problem 2: As shown in Fig. 1(b), a two-segment airfoil with a chord length c has a slope angle a.. Surface pressures on the two upper surfaces are p1 and p3, respectively. The pressure on the lower surface is p2. Calculate the lift and drag of the flat-plate airfoil. Note: Decompose pressure vectors into the vertical and horizontal components that contribute to the lift and drag, respectively. The chord length c is a distance between the leading and trailing edges. You need to calculate the length of a segment. a (a) pl p2 p2 a pl (b) p3
- A sprinkler system pumps water through a large pipe inlet with a diameter (di). The pipe then breaks into N narrow pipes (which have a diameter, o, and a length, L2), before the water is released to the atmosphere, as shown in figure Q4. The entrance to the small pipe from the large pipe has a loss coefficient of K. You may assume the flow is laminar and fully developed everywhere in the system, and that any changes in height are negligible. The viscosity is not negligible. a) Find an expression for the velocity of water leaving the sprinkler. b) Find an expression for the gauge pressure at point A, a distance Lt upstream of the narrow pipes. Express your answer in terms of the flowrate, Q.A very small circular cylinder of radius Ri is rotating at angular velocity ?i inside a much larger concentric cylinder of radius Ro that is rotating at angular velocity ?o. A liquid of density ? and viscosity ? is confined between the two cylinders. Gravitational and end effects can be neglected (the flow is two-dimensional into the page). If ?i = ?o and a long time has passed, generate an expression for the tangential velocity profile, u? as a function of (at most) r, ? ,Ri, Ro, ?,and ?, where ? = ?i = ?o. Also, calculate the torque exerted by the fluid on the inner cylinder and on the outer cylinder.B
- please helpA thin-walled hollow spherical ball of mass 0.4 kg and radius 0.1m is filled with alcohol of density 800 kg/m3. It is released from the bottom of a pool filled with water. a. sketch a FBD for the ball b. write out newtoon's 2nd law equation c. Find the acceleration of the ballQ. 26. A cylindrical tank having radius R is half filled with water having density p. There is a hole at the top of the tank. The tank is moved horizontally, perpendicular to its length, with a constant acceleration equal to the acceleration due to gravity (g). Find the maximum pressure exerted by water at any point on the tank. Atmospheric pressure is Po. Assume that there is no spillage.