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A fluid flow enters the plane-wall diffuser that has an entrance area of A0 at a velocity of U0. (a) Assuming the fluid is inviscid. determine the velocity gradient
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Engineering Mechanics: Statics
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- Liquid is pushed through the narrow gap formed between two glass plates. Thedistance between the plates is h and the width of the plate is b . Assuming that theflow is laminar, two-dimensional and fully developed, derive a formula for thelongitudinal pressure gradient in terms of the volumetric flow rate, Q, the fluid viscosityand the distances b and h .In an example the above conditions apply with b = 0.10 m and h = 0.00076 m. Theliquid is glycerine that has an absolute viscosity of 0.96 N s/m². A pressure differenceof 192 kN/m² is applied over a distance of 0.24 m. Calculate the maximum velocity thatoccurs in the centre plane of the gap and the mean velocity.Answer 0.06 m/sarrow_forwardA viscous fluid of viscosity 2.48 Pa-s and density 884 kg/m³ is dragged by a rigid flat surface that moves upward with speed V, as shown. The velocity profile in the fluid layer is of the form, pg v(x) = (x? – 2hx) + V Find the minimum speed V for which the entire fluid layer moves upward. What are the minimum and maximum values of the shear stress in the layer? Assume the flow to be incompressible and fully developed. 5 mmarrow_forwardOil flows between two very long parallel plates, separated from H, with width b. The bottom plate moves with speed U and is isolated. The upper plate is at rest and receives heat from the environment at a rate equal to qs". Consider laminar flow, thermally developed. Due to the high viscosity of the fluid, viscous dissipation is relevant U isolada 1 - Estimate the velocity profile considering the null pressure gradient and determine the average speed. 2. Determine dissipation per volume unit. 3. Set mixing temperature and determine the mixing temperature variation over the plates.arrow_forward
- Assume the temperature of the exhaust in an exhaust pipe can be approximated by T = To (1 + ae-bx) [1 + c cos(@t)], where To = 100 °C, a = 3, b = 0.03 m ¹, c = 0.066, and w = 100 rad/s. If the exhaust speed is a constant 3 m/s, determine the time rate of change of temperature of the fluid particles at (a) x = 0 and (b) x = 4 m when t = 0. DT (a) °C/s (b) Dt DT Dt = °C/sarrow_forwardOne dimensional flow occurs in the circular tube at the location adequately far from the entrance shown in the figure right. Velocity profile is the laminar and expressed as; U(x) = Umax (1-r/R?) Where R: radius of the tube, r: distance beginning from the center and Umax : maximum velocity (at the center). Drive the expression for the drag force per unit area applied to both plates by the flu id (F/A). If the drag force is 0.565 N, calculate the necessary velocity for the water at 20°C flow through the tube with the radius of 0.08 m and 15 m length (u:0.0010 kg/m. s). R -Umaxarrow_forward5. A linear velocity profile is formed in a fluid between two plates as shown in the figure when one of the plates is moved parallel to the other and there is no externally imposed pressure gradient (i.e. there is no pump). If the top plate is travels at U = 0.3 m/s and the bottom plate is held fixed and the two plates are separated by a distance d = 0.3 m/s, derive an equation for the velocity profile u(y). Assume that the fluid in contact with either plate moves at the same speed as the plate (this is called the no-slip condition). U=0.3 m/s d=0.3 marrow_forward
- 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:arrow_forward2. Show that the two-dimensional flow described (in meter-second units) by the equation y = x + 2x² – 2y² is irrotational. What is the velocity potential of the flow? If the density of the fluid is 1.12 kg m and the piezometric pressure at the point (1, -2) is 4.8 kPa, what is the piezometric pressure at the point (9, 6)? -3arrow_forwardWater flows through the following circular pipe with a diameter of 30 mm at a speed of 3 m/s, what is the hydrodynamic entry length? The water dynamic viscosity is 1.002×10-3kg/(m⋅s).arrow_forward
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