for two-dimensional, uncompressed, irrotational flow, examine the superposition of double flow with uniform flow (flow through cylinder)
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Question: for two-dimensional, uncompressed, irrotational flow, examine the superposition of double flow with uniform flow (flow through cylinder)
(a) flow function and velocity potential.
(b) Speed field.
(c) stopping points.
(d) cylinder surface.
(e) surface pressure distribution.
(f) the pulling force on the circular cylinder.
(g) buoyancy on the circular cylinder.
Please solve d), e), f), g)
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- Mott ." cometer, which we can analyze later in Chap. 7. A small ball of diameter D and density p, falls through a tube of test liquid (p. µ). The fall velocity V is calculated by the time to fall a measured distance. The formula for calculating the viscosity of the fluid is discusses a simple falling-ball vis- (Po – p)gD² 18 V This result is limited by the requirement that the Reynolds number (pVD/u) be less than 1.0. Suppose a steel ball (SG = 7.87) of diameter 2.2 mm falls in SAE 25W oil (SG = 0.88) at 20°C. The measured fall velocity is 8.4 cm/s. (a) What is the viscosity of the oil, in kg/m-s? (b) Is the Reynolds num- ber small enough for a valid estimate?Question 11) Vortices are usually shed from the rear of a cylinder, which are placed in a uniform flow at low speeds. The vortices alternatively leave the top and the bottom of the cylinder, as shown in figure, causing an altemating force normal because of generating a dimensionless relationship for Kánmán vortex shedding frequency f (1/s) as a function of free-stream speed V(7m/s), fluid density p (kgm³), fluid viscosity µ (kg/m.s), sound velocity c (m/s), surface roughness & (m) and cylinder diameter D(m). || I-Determine the nondimensional a parameters using repeating variables, involving f, , c and u as nonrepeating variables ii-the dynamics of Bhosphorus bridge is investigated in a wind tunnel for the vortex generation behind the wires. A 1/59 scaled down model of the hanging wires is used in the laboratory. If vortex shedding frequency of of Bhosphorus bridge 590 Hz is measured in the laboratory at 29 m/s. Then detemine the expected frequency in the actual case exposed to 190 km/h…One of the conditions in using the Bernoulli equation is the requirement of inviscid flow. However there is no fluid with zero viscosity in the world except some peculiar fluid at very low temperature. Bernoulli equation or inviscid flow theory is still a very important branch of fluid dynamics for the following reasons: (i) (ii) There is wide region of flow where the velocity gradient is zero and so the viscous effect does not manifest itself, such as in external flow past an un- stalled aerofoil. The conservation of useful energy allows the conversion of kinetic and potential energy to pressure and hence pressure force acting normal to the control volume or system boundary even though the tangential friction stress is absent. It allows the estimation of losses in internal pipe flow. (A) (i) and (ii) (B) (i) and (iii) (ii) and (iii) All of the above (C) (D)
- Ius A fluid flow situation depends on the Nelocity (V), the density several lineor dimension, 4shi, h2.pressure drep (DO > gravity (9) , Viscosity , Susface tension ). and bulk mo dulus of elasticity k. Apply dimen sional analysis. to these variables td A s*Using II-Theorem method to Express (n) in terms of dimensionless groups.The efficiency (n) of a fan depends upon density (p), and dynamic viscosity (u), of the fluid, angular velocity (@), diameter of the rotator (D), and discharge (Q). Q3/ A petroleum crude oil having a kinematics viscosity 0.0001 m?/s is flowing through the piping arrangement shown in the below Figure,The total mass flow rate is equal 10 kg/s entering in pipe (A) . The flow divides to three pipes ( B, C, D). The steel pipes are schedule 40 pipe. note that the dynamic viscosity 0.088 kg/m.s. Calculate the following using SI units: 1- The type of flow in pipe (A). 2- The mass velocity in pipe (B) GB. 3- The velocity in pipe (D) Up. 4- The Volumetric flow rate in pipe (D) QD. 5- The Volumetric flow rate in pipe (C) Qc. Og = 2o mm Ug = 2UA Perolenm crude oIL A ma = 1o Kg/s O = 5o mm mic = ? Go = 7000 k9/m.s Nate that!- O, = 30 mm. D:0iameter. U:velocity G mass velocity mimass How vateA boundary layer is a thin region (usually along a wall) in which viscous forces are significant and within which the flow is rotational. Consider a boundary layer growing along a thin flat plate. The flow is steady. The boundary layer thickness ? at any downstream distance x is a function of x, free-stream velocity V∞, and fluid properties ? (density) and ? (viscosity). Use the method of repeating variables to generate a dimensionless relationship for ? as a function of the other parameters. Show all your work.
- In the study of turbulent flow, turbulent viscous dissipation rate ? (rate of energy loss per unit mass) is known to be a function of length scale l and velocity scale u′ of the large-scale turbulent eddies. Using dimensional analysis (Buckingham pi and the method of repeating variables) and showing all of your work, generate an expression for ? as a function of l and u′.1. Explain the importance in CFD of the following equations. Some important linear partial differential equations in fluid dynamics are : a?u a²u 1. 1-D wave equation 2. 1-D heat conduction equation k where a : (PC, ) a’u a?u ôx? ' ây? = v?u = 0 3. 2-D Laplace equation + .2 a²u a²u 4. 2-D Poisson equation v²u = f(x,y) ây? + a²u a?u_ a²u 5..3-D Laplace equation = v? u = 0 + ay? ' ôz?Q1: Consider laminar flow over a flat plate. The boundary layer thickness o grows with distance x down the plate and is also a function of free-stream velocity U, fluid viscosity u, and fluid density p. Find the dimensionless parameters for this problem, being sure to rearrange if neessary to agree with the standard dimensionless groups in fluid mechanics. Answer: Q2: The power input P to a centrifugal pump is assumed to be a function of the volume flow Q, impeller diameter D, rotational rate 2, and the density p and viscosity u of the fluid. Rewrite these variables as a dimensionless relationship. Hint: Take 2, p, and D as repeating variables. P e paD? = f( Answer:
- A viscous fluid of density 1200 kg/m3 and viscosity 0.9 Pa.s is confined in a spacing of 0,01 m between two parallel and horizontal plates of length 0,6 m and width 0,6 m. The upper plate is pulled with a uniform and steady speed of 0,7 m/s in its own plane. The lower plate is stationary. Viscous fluid flow is laminar steady and incompressible. a) What is the magnitude of mass flow rate in spacing (in kg/s)? b) What is the magnitude of maximum shearing stress in the flow field (in Pa)? c) What is the frictional force over the lower plate surface (in N )? d) What is the frictional power lost in pulling the upper plate (in W)?Taylor number (Ta) is used here to describe the ratio between the inertia effect and the viscous effect. By applying Buckingham Pi's Theorem, determine an equation for Ta as a function of the radius of inner cylinder (r), cylinder tangential velocity (v), fluid dynamic viscosity (u), gap distance (L) and fluid density (p). Q43.) Transport review: For steady-state flow of water in a stationary pipe of radius R, simplify the Navier-Stokes equation to a simple 2nd order ODE. Assume a pressure drop AP over the length of the pipe (L). What are two boundary conditions that can be used? Do not solve.