Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free- stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a boundary layer disturbance thickness of = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad). y U control volume boundary-layer region a flat plate d U δ u(y)

Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free- stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a boundary layer disturbance thickness of = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad). y U control volume boundary-layer region a flat plate d U δ u(y)

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.30P: Air at 1000C flows at an inlet velocity of 2 m/s between two parallel flat plates spaced 1 cm apart....

See similar textbooks

Similar questions

Engine oil at 100C flows over and parallel to a flat surface at a velocity of 3 m/s. Calculate the thickness of the hydrodynamic boundary layer at a distance 0.3 m from the leading edge of the surface.
Air at 20C flows at 1 m/s between two parallel flat plates spaced 5 cm apart. Estimate the distance from the entrance to the point at which the hydrodynamic boundary layers meet.
Evaluate the Nusselt number for flow over a sphere for the following conditions: D=0.15m,k=0.2W/mK, hc=102W/m2K.
Flow straighteners consist of arrays of narrow ducts placed in a flow to remove swirl and other transverse (secondary) velocities. One element can be idealised as a square box with thin sides as shown below. Calculate the pressure drop across a box with L=22 cm and a= 2.7 cm, if air with free-stream velocity of Uo = 11 m/s flows though the straightener. Use laminar flat-plate theory and take u = 1.85 x 10-5 Pa.s and p = 1.177kg/m³ . %3D %3D a Uo Figure 1: Flow across straighteners.
PART A -5 For Air Assume: v=1.46×10 m²/s and p =1.225 kg/m³ Question A1 A flat plate with unit width is placed in a uniform steady two-dimensional flow of air with negligible pressure gradient. The velocity distribution of the boundary layer forming on either side of this plate has been given as: U /Us = 2.0(y/ 8) - (y/8)2.0, where U = 10 m/s. 1- Find and expression for the boundary layer thickness as a function of Rex. 2- At x=1.0 m calculate the shear stress corresponding to the points y=0.0,3.0 and 10.0 mm. 3- Calculate the boundary layer displacement and momentum thicknesses at x=1.0m. By using the calculated momentum thickness determine the drag force acting on one side of the plate between its leading edge and x = 1.0m. 4- At x=1.0m, calculate the mass flow rate through the boundary layer (mkg/s per unit width of the plate). What is the corresponding mass flow rate if the flow was inviscid (m; kg/s per unit width of the plate)? 5- By using appropriate equation (s) explain how the…
Problem 6. A boundary layer is developing for uniform flow of air at STP over a flat plate as shown. The free-stream flow outside the boundary layer has an undisturbed velocity of U = 50 m/s. The plate has a width of b = 3.0 m perpendicular to the schematic. A control volume (CV) with control surfaces (ab), (bc), (cd), and (ad) is defined as shown. Assume that the flow in the boundary layer is turbulent at surface (cd) with a 1/7th power-law velocity profile and a boundary layer disturbance thickness of 8 = 2.0 cm. For surfaces (ab), (bc), and (cd), calculate (a) mass flowrate and (b) momentum transported (in Newtons). (c) Determine the drag for the flat plate at surface (ad). U U control volume u(y) boundary-layer region flat plate a
A two-dimensional diverging duct is being designed to diffuse the high-speed air exiting a wind tunnel. The x-axis is the centerline of the duct (it is symmetric about the x-axis), and the top and bottom walls are to be curved in such a way that the axial wind speed u decreases approximately linearly from u1 = 300 m/s at section 1 to u2 = 100 m/s at section 2 . Meanwhile, the air density ? is to increase approximately linearly from ?1 = 0.85 kg/m3 at section 1 to ?2 = 1.2 kg/m3 at section 2. The diverging duct is 2.0 m long and is 1.60 m high at section 1 (only the upper half is sketched in Fig. P9–36; the halfheight at section 1 is 0.80 m). (a) Predict the y-component of velocity, ?(x, y), in the duct. (b) Plot the approximate shape of the duct, ignoring friction on the walls. (c) What should be the half-height of the duct at section 2?
Using the theory on boundary layer and flow separation, explain how the pressure drop across a sudden contraction is not equal to the change in velocity of the fluid. Relate this to how conical reducers are more preferred than a flanged contraction shown in the figure below. Direction of flow C-C Plone of vena contracto
A flat plate at zero angle of attack is in a 50° F airflow, at a speed of 260 ft/s. The plate is 4 ft by 10 ft. The goal is to determine what orientation of the plate in the stream leads to minimum drag force. To determine that, compute Re and then CfL for configuration (a) (Flow is parallel to the long dimension.), and then for configuration (b) (Flow is parallel to the short dimension.) Which orientation turns out to have the lesser drag?
We are testing a flat plate of length L = 1.125 m and width W = 0.225 m in a stream of air flowing with a velocity of 20 m/s. In test case 1, the air is flowing parallel to L and in test case 2 air is flowing parallel to W. Find: What portion of the boundary layer flow is laminar in each case? What is the highest laminar boundary layer thickness in each case? Assuming the flow is entirely turbulent over the plate, calculate the drag force in both test cases Take air density as 1.2 kg/m3 and its viscosity as μ=18×10−6μ=18×10−6 N.s/m2.
**75. ssm A uniform rectangular plate is hanging vertically downward from a hinge that passes along its left edge. By blowing air at 11.0 m/s over the top of the plate only, it is possible to keep the plate in a horizon- tal position, as illustrated in part a of the drawing. To what value should the air speed be reduced so that the plate is kept at a 30.0° angle with re- spect to the vertical, as in part b of the drawing? (Hint: Apply Bernoulli's equation in the form of Equation 11.12.) A Moving air 130.0 Hinge Edge view of plate (a) (b)
Hand written plz asap i'll give you multiple upvote