The velocity distribution for the shear flow shown between two plates of gap a is giv 1 dp (y² – ay) +-y U u(у) 2µ dx а What is the pressure gradient that will result in a zero shear stress at the lower wall

The velocity distribution for the shear flow shown between two plates of gap a is giv 1 dp (y² – ay) +-y U u(у) 2µ dx а What is the pressure gradient that will result in a zero shear stress at the lower wall

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

See similar textbooks

Similar questions

rerce D6 =blank Dimetr Yedaction Fn =0015 Y(Pi-CDp Ev-vam velocity PP- Panch Diametr FELt Ye Sreching force woling force drawing foreo 2. 25 ower Kx=0.98+o.02 Rd=die corner vadus mui die shape facArin extrustion -Lentn tthicknes YA=Stess ) Dirct on 1 The data given in Table Q1(a) corresponds to a cold heading operation performed to make square head on a steel bolt. Figure Q1(a) shows the dimensions of the bolt to be produced. Strength coefficient for the steel Table Q1(a) Strain hardening exponent 550 MPa Coefficient of friction at the die-work interface- 0.21 Thickness of wire stock out of which the bolt is made 0.16 Final length of the bolt. 10 mm 120 mm Compute: (i) The length of stock must project out of the die in order to provide sufficient volume of material for this upsetting operation. (ii) The total number of bolts that can be made out of 6 m rod (wire stock) (iii) The maximum force that the punch must apply to form the head 5 mm 10 mm 15 mm Figure Q1(a)
4s-1, Given the velocity field V = Axî – Ayĵ, where A %3D (a) Sketch the velocity field. (you can do this by hand or use software of your choice)
PROPERTIES OF FLUIDS 0 The fluid flowing in Fig. 1-3 has an absolute viscosity (u) of 0.0010 lbs/ft² and specific gravity of 0.913. Calculate the velocity gradient and intensity of shear stress at the boundary and at points 1 in, 2 in, and 3 in from the boundary, assuming (a) a straight-line velocity distribution and (b) a parabolic velocity distribution. The parabola in the sketch has its vertex at A and origin at B. 3" B V ບ 45 in/s V Fig. 1-3
1) The velocity profile of a viscus fluid over a plate is parabolie with vertex 25 em from the plate ,where the velocity 125 cm/s. calculate the velocity gradient and shear stress at distance of (0, 5, 15 and 25 cm) from the plate given the viscosity of the fluid =7 poise ? Also draw the figure explain the relationship between the velocity gradient and shear stress. Take velocity profile for parabolic equation, (v = ay + by + c)
Calculate velocity gradients and shear stress for y = 0.0, 0.2, 0.4, and 0.6 m, if the velocity profile is a quarter-circle having its center 0.6 m from the boundary (See figure below). The fluid viscosity is 7.5 x 10-4 Ns/m2. y The velocity profile is given by (, + 0.6m -- 1) = 1 10 m/s 0.6 m
Air at 20 °C forms a boundary layer near a solid wall, in which the velocity profile is sinusoidal (see Fig. 1-14). The boundary-layer thickness is 7 mm and the peak velocity is 9 m/s. Compute the shear stress in the boundary layer at y equal to (a) 0, (b) 3.5 mm, and (c) 7 mm. 7 mm Vmax = 9 m/s Peak Sine wave Fig. 1-14
Orange JO A O X 91|4 2:26 ch1_introductio.. Shear stress (t) is the resistance per unit area of the upper plate t = R/A=T/A Water responds to shear stress by continuously yielding in angular deformation in the direction of the shear. IThe rate of angular deformation in the fluid, d(8)/dt ,is proportional to the shear Istress, as shown in Figure 1.1. do dt dx ,and v = dy dx Angular deformation (Shear strain), 0 = dt do Rate of shear strain = dt dx dv (Velocity gradient) dy dy dt dv Therefore, to dv T = constant dy dv T = - dy The proportionally constant, u, is called the absolute viscosity of the flyid Example A flat plate of 50 cm² is being pulled over a fixed flat surface at a constant velocity of 45 cm/sec (Figure 1.1). An oil film of unknown viscosity separates the plate and the fixed surface by a distance of 0.1 cm. The force (T) required to pull the plate is measured to be 31.7 N, and the viscosity E of the fluid is constant. Determine the viscosity (absolute). 22 Example A flat…
Q3: A very lange thin plate is centered in a gap of width Co.06 m) with different oils of unknown viscosities above & below , one viscosity is twice the other. When the p late is pulled at a velocity of Co-3 mls.), the resulting force on one square meter of the plate due fo the viscous shear on both sides is C29 N). Calculate the viscosities of the oils.
valg, (21535mm 1.15 The pressure difference, Ap, across a partial blockage in an artery (called a stenosis) is approximated by the equation μV Ap - K. 4 + K.(A-1) pv² = K₂ A s.r to zogy nish190 32\V as bonb dignol a 3 basiy noft where V is the blood velocity, u the blood viscosity (FL-2T), p the blood density (ML), D the artery diameter, Ao the area of the unobstructed artery, and A, the area of the stenosis. Determine the dimensions of the constants K, and K. Would this equation be valid in any system of units?
4) The increase of temperature results in (a) increase in viscosity of gas (d) decrease in viscosity of liquid 5) Consider the flow in pipe in figure. If P₁ -AP/y. b) The ow direction is from 2 to 1 if AZ v3 (b) p3>pl; vl > v3 (d) p4 vl (c) p2>p3; v2> v3 (e) p4> pl; v4
Fluid Mechanics II Sheet NO (04) Damietta University Faculty of Engineering Mechanical Engineering Dept. FACULTY OF ENGINEERING DAMIETTA UNIVERSIm bluas daola-dunigil us 3- Fluid flow between two horizontal infinite parallel plates with a spacing of H mm shown in figure 3. Determine the volume flow rate per width and the shear stress on upper and lower plates. U2 , draw the velocity profile distribution. U1 Moving plate H Moving plate U2 Figure 3 , a tornado can be approximated As illustrated in Fig. 4 by a free vortex of strength I' for r > Re, where R̟ is the radius of the core. Velocity measurements at points A and B indicate that V = 125 ft/s and V3 = 60 ft/s. Determine the distance from point A to the center of the tornado. Why can the free vortex model not be used to approximate the tornado throughout the flow field (r > 0)? 4- B +100 ft- Figure 4
The following rheological data were collected on a new "Thick 'n Spicy" brand of tomato catsup at 20°C and 90 kPa. rate of shear (s") shear stress (Pa) 10.0 20.4 20.0 21.5 40.0 23.0 60.0 25.0 80.0 26.5 (a) Plot these measured values on graph-paper. Which class of fluid does the catsup belong to?