Please show all work!! A thin wing with a parabolic chord distribution is flying at speed U∞ and zero angle of attack, asshown below. The fluid has density p and viscosity μ. Determine the drag force, D, and the dragcoefficient, Cp = D(US), where S is the planform area of the wing. Assume laminar flow andexpress your drag coefficient answer in terms of the Reynolds number based on a, Re₁ = U∞a/v.U∞TOP VIEWS = areab|c(y) = quadraticy

Given1. Flight Speed: U∞2. Fluid Properties:Density ρViscosity μ3. Wing Dimensions:Wing has a…

Answered: A thin wing with a parabolic chord…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A thin wing with a parabolic chord distribution is flying at speed U∞ and zero angle of attack, asshown below. The fluid has density ρ and viscosity μ. Assume that the flow starts laminar at theleading edge but then transitions to tubulent at xcrit = 0.25a. a) Sketch the regions of laminar and turbulent flow over the wing. Calculate and label relevantdistances.b) Determine the drag force, D, and the drag coefficient, CD ≡ D/((1/2) ρU2∞S), where S is theplanform area of the wing. Express your drag coefficient answer in terms of the Reynoldsnumber based on a, Rea ≡ (U∞a)/nu.
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A 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 mm
Draw the diagram of the dimensionless velocity profile and 11 for the boundary layer on the surface under the pressure gradient and discuss the diagrams by fully mentioning the parameters
1. The Stokes-Oseen formula for drag force Fon a sphere of diameter D in a fluid stream of low velocity V, density p, and viscosity u is: 9T F = 3TuDV + 16PD? Is this formula dimensionally homogenous? 2. The efficiency n of a pump is defined as the (dimensionless) ratio of the power required to drive a pump: QAp input power Where Q is the volume rate of flow and Ap is the pressure rise produced by the pump. Suppose that a certain pump develops a pressure of Ibf/in? (1ft = 12 in) when its flow rate is 40 L/s (1L =0.001 m). If the input power is 16hp (1hp = 760 W), what is the efficiency?
A model of an aircraft is being tested in a wind-tunnel. If the model was replaced by one that is half the size but is otherwise identical, what would be the ratio of the drag on the large model to the drag on the small model for exactly the same flow conditions. Give your answer to two decimal places. The model is in a region where drag coefficent is independent of Reynolds number.
E
A solid cone of angle 2Ɵ, base r 0 , and density ρ c is rotating with initialangular velocity ω 0 inside a conical seat,as shown below. The clearance h is filled with oilof viscosity μ. Neglecting air drag, derive an analytical expression for thecone’s angular velocity ω(t) if there is noapplied torque.
Two infinite plates a distance h apart are parallel to the xzplane with the upper plate moving at speed V, as inFig. There is a fluid of viscosity μ and constant pressurebetween the plates. Neglecting gravity and assumingincompressible turbulent flow u(y) between the plates, usethe logarithmic law and appropriate boundary conditions toderive a formula for dimensionless wall shear stress versusdimensionless plate velocity. Sketch a typical shape of theprofile u(y).
QUESTION 6 Above a flat plate, a steady and two-dimensional laminar boundary layer grows without pressure gradient. At x₁ = 0.3 m from the flat plate leading edge, the boundary layer has tickness ō. Assuming a cubic self-similar velocity profile, determine the distance x2 at which the boundary layer thickness is 1.7 times that at x₁. State your answer in metres to three decimal places and enter the numerical value only.
(a) Use the y-momentum equation to show that the pressure gradient across the boundary layer is approximately zero i.e. = 0 . Assume the boundary layer to be a two-dimensional ду steady and incompressible flow. Neglect gravitational forces. State clearly all assumptions made. Use the Bernoulli's equation to prove that the pressure difference is given by (b) P2-P1 = -4pU? for a fluid with constant density p flowing from point 1 to point 2 where pi, U1, A1 are the pressure, velocity and flow cross-section area at point 1 and p2, U2, A2 are the pressure, velocity and flow cross-section area at point 2 respectively. The ratio of the cross-section area A1 = 3.
i have fluid mechanics exam tomorrow but i couldnt understand first 3 part of that question. thank you so much who can solve this for me .

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