A fluid with specific weight of 12000 N/m³ and viscosity of 0.002 kg/m.s flows between two parallel plates as shown in the figure. The upper plate moves with the velocity of U and the lower plate is fixed. (a) Find the velocity profile u(y) in terms of h, U, and dp/dx. Assume the flow is steady, 2D, and parallel to the plates. (b) A manometer is used to measure the pressure drop Ap = P2 - pi of the flow. Find Ap if the elevation difference in the manometer is H=0.2 cm and ym=16000 N/m³. (c) Assuming dp/dx = Ap/L, find the fluid velocity at y=h/2. Consider h=2.5 cm, L=15 cm, and U=0.007 m/s.

3. Water flowing through a pipe assumes a laminar-flow velocity profile at some section is parabolic: u(0) -4J Figure 2 where u(r) is the velocity at any position r, ß is a constant,-11s the viscosity of water, and r is the radial distance from the pipe centerline. (a) Develop an equation for u(r) assuming a parabolic velocity profile and using the known velocities at the walls u(ro)-0 and the center u(0) (Just use symbols). (b) Develop an equation for shear stress in the fluid at the wall of the pipe (Just use symbols). (c) If the given profile persists a distance L along the pipe, what is the force on the wall due to the moving water and what is its direction? (Hint: The force on the wall is equal in magnitude but in the opposite direction of that in the fluid.)

A liquid of density 1150 kg/m3 flows steadily through a pipe of varying diameter and height. At Location 1 along the pipe, the flow speed is 9.47 m/s and the pipe diameter d1 is 11.7 cm. At Location 2, the pipe diameter d2 is 17.7 cm. At Location 1, the pipe is Ay=8.19 m higher than it is at Location 2. Ignoring viscosity, calculate the difference APbetween the fluid pressure at Location 2 and the fluid pressure at Location 1.

A constant-thickness film of viscous liquid (SG = 0.8, μ = 0.5 Pa-s) flows down an inclined plate an angle of 10⁰ as shown in the figure The velocity profile is given by the equation, u(y) = Cy(2h — y). If the value of his 5 cm, what is the value of the maximum velocity in m/s? NOTE: The pressure does not vary along the flow direction. u(y) Answer:

can someone explain why P is a function if time only for this question

[4] Consider steady, incompressible, laminar flow of a Newtonian fluid in the narrow gap between two infinite parallel plates. The top plate is moving at speed V, and the bottom plate is stationary. The distance between these two plates is he, and the gravity acts in the negative z-direction (in to the page). There is no applied pressure other than hydrostatic pressure due to gravity. This flow is called Couette flow. Calculate the velocity and pressure fields, and estimate the shear force per unit area acting on the bottom plate. Moving plate Flui Finod plate

Consider a steady, two-dimensional, incompressible fl owof a newtonian fl uid in which the velocity fi eld isknown: u = - 2 xy , υ = y 2 - x 2 , w = 0. ( a ) Does thisfl ow satisfy conservation of mass? ( b ) Find the pressurefi eld, p ( x , y ) if the pressure at the point ( x = 0, y = 0) isequal to p a .

A potential steady and incompressible air flow on x-y plane has velocity in y-direction v= - 6 xy . Determine the velocity in x-direction u=? and Stream Function SF=? ( x2 : square of x ; x3: third power of x ; y2: square of y , y3: third power of y)ANSWER: u= 3 x2 - 3 y2 SF= 3 x2 y - y3

A capillary tube has an 8mm inside diameter through which liquid fluorine refrigerant R-11 flows at a rate of 0.03 cm3/s. The tube isto be used as a throttling device in an air conditioning unit. A model of this flow is constructed by using a pipe of 3cm inside diameter and water as the fluid medium. (Density of R-11 = 1.494 g/cm3 and its viscosity is 4.2 x10-4 Pa.s; Density of water is 1g/cm3 and its viscosity 8.9 x10-4 Pa.s)a) What is the required velocity in the model for dynamic similarity? Hint: For flow through a tube the Ne number can be expressed in terms of the Reynolds numberb) When dynamic similarity is achieved the pressure drop is measured at 50 Pa. What is the corresponding pressure drop in the capillary tube?Hint: In this case the Euler number defines dynamic similarity with reference to the static pressure drop

An oil film drains steadily down the side of a vertical wall, as shown on figure below. After an initial development at the top of the wall it attains a fully-developed draining vertical oil- film wherein the film becomes independent of "z" and of constant wall thickness. Let the vertical velocity as (w) and using the nomenclatures in the figure such as distance from plate (x), fluid properties, gravity (g) and film thickness (  ).   Perform dimensional analysis and determine the function in terms of dimensionless parameters.