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r a square array array derive the equation for fiber volume fraction with fiber radius of...
Q1) For a unidirectional carbon fiber reinforced lamina composites, fiber volume fraction 0.65, En-300 GPa, En...
Q1) For a unidirectional carbon fiber reinforced lamina composites, fiber volume fraction 0.65, En-300 GPa, En = 30 G Pa, Gn2-40 G Pa while for matrix, Gm-10 GPa, Em-3 GPa Determine the longitudinal and transverse moduli of the composites, and the shear modulus of the composites.
ㆍ 2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0...
ㆍ
2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0, uee 7:2 where is the zenith angle and assume u is independent on the azirnuth angle o. a) By separation of variables, derive two ordinary differential equations of r and w=Cos given by r2 F(r)2r F(r)-n(n+ 1)F(r) 0, (1- w2)G (w)- 2wG (w)n(n +1)G(w) 0. (n 0,1,2,.) b) Find Fn (r) and Gn (w) satisfying Gn(1) =1 for...
1. A fishing rod is made of fiberglass/epoxy composites with a circular cross R. The volume...
1. A fishing rod is made of fiberglass/epoxy composites with a circular cross R. The volume fraction of the continuous filaments in the composite is os continuous filaments in the composite is 0.5 and each fiber the elastic modulus of the fiber is 10 Msi and the matrix has a radius r. Suppose R = 1000r, the elastic modulus of the fiber is 10 is 0.5 Msi. The ultimate strength of the fiber is 50 ksi. (a) Calculate the number...
Problem #2 .Calculate the volume and surface area of a torus from the minor radius r...
Problem #2 .Calculate the volume and surface area of a torus from the minor radius r and major radius R. The equation for the volume of a torus i:s and the equation for the surface area of a torus is A = 4㎡Ar Your script should read-in values for the minor radius and major radius and display the calculated values with appropriate units. The units should also be read-in. Test your program for the following two cases: . Or-5in and...
1. Derive a power series solution of the ordinary differential equation de in powers of r Find th...
1. Derive a power series solution of the ordinary differential equation de in powers of r Find the radius of convergence of the series.
1. Derive a power series solution of the ordinary differential equation de in powers of r Find the radius of convergence of the series.
A disk of mass M and radius R is rotating with an angular velocity ω. A...
A disk of mass M and radius R is rotating with an angular velocity ω. A rod also of mass M but length 2R is initially not rotating. It is dropped vertically onto the rotating disk. After the collision, the disk and rod rotate together with an angular velocity of? What fraction of the initial kinetic energy was lost in the collision?
5. (**) Field of a uniform ring of charge The ring of radius R shown at...
5. (**) Field of a uniform ring of charge The ring of radius R shown at right lies in the yz-plane and carries a uniformly distributed charge Q. (a) Find the electric field due to the ring of charge at any point on the X-axis. (b) Find the value of x for which the electric field is a maximum, and determine this maximum field strength. (c) On the axes below, sketch the magnitude of Ex versus x for points on...
(2, Consider the Laplace equation for a ball of radius R described in spherical coordinates (T,0) 2 1 +00n3 2 0 wher...
(2, Consider the Laplace equation for a ball of radius R described in spherical coordinates (T,0) 2 1 +00n3 2 0 where 0 is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w =cos e given by 12 F" (T) +2r F (r) - n(n + 1 ) Fr (r) = 0, (1 w2)G (w) - 2wG (w) + n(n+ 1)G, (w)...
Using this table determine the van der Waal radius for Ar. Then use this radius to determine the fraction of volume occu...
Using this table determine the
van der Waal radius for Ar. Then use this radius to determine the
fraction of volume occupied by 1 mol of argon at 25C and 1 atm.
Table 17.2 Lennard-Jones Parameters for Atoms and Molecules Particle e/kJ mol-1 o/Å 0.997 1.77 0.307 0.765 0.943 3.40 4.10 2.93 3.92 3.65 4.33 3.82 1.65 1.23 2.02 C6H6 8.60
#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value o...
Fluid Mechanics
#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value of r (as a fraction of R) that maximizes u(r). How does this value of velocity compare with Vc? Compute the wall shear stress, du or Perform a control volume analysis on a pipe section of length e. Relate the pressure drop across the pipe section to the shear stress. Substitute the relation above for tw to...
Q1) For a unidirectional carbon fiber reinforced lamina composites, fiber volume fraction 0.65, En-300 GPa, En = 30 G Pa, Gn2-40 G Pa while for matrix, Gm-10 GPa, Em-3 GPa Determine the longitudinal and transverse moduli of the composites, and the shear modulus of the composites.
ㆍ
2 Consider the Laplace equation for a ball of radius R described in spherical coordinates (r,0) 2 urrt r cot ug=0, uee 7:2 where is the zenith angle and assume u is independent on the azirnuth angle o. a) By separation of variables, derive two ordinary differential equations of r and w=Cos given by r2 F(r)2r F(r)-n(n+ 1)F(r) 0, (1- w2)G (w)- 2wG (w)n(n +1)G(w) 0. (n 0,1,2,.) b) Find Fn (r) and Gn (w) satisfying Gn(1) =1 for...
1. A fishing rod is made of fiberglass/epoxy composites with a circular cross R. The volume fraction of the continuous filaments in the composite is os continuous filaments in the composite is 0.5 and each fiber the elastic modulus of the fiber is 10 Msi and the matrix has a radius r. Suppose R = 1000r, the elastic modulus of the fiber is 10 is 0.5 Msi. The ultimate strength of the fiber is 50 ksi. (a) Calculate the number...
1. Derive a power series solution of the ordinary differential equation de in powers of r Find the radius of convergence of the series.
1. Derive a power series solution of the ordinary differential equation de in powers of r Find the radius of convergence of the series.
5. (**) Field of a uniform ring of charge The ring of radius R shown at right lies in the yz-plane and carries a uniformly distributed charge Q. (a) Find the electric field due to the ring of charge at any point on the X-axis. (b) Find the value of x for which the electric field is a maximum, and determine this maximum field strength. (c) On the axes below, sketch the magnitude of Ex versus x for points on...
(2, Consider the Laplace equation for a ball of radius R described in spherical coordinates (T,0) 2 1 +00n3 2 0 where 0 is the zenith angle and assume u is independent on the azirnuth angle d. a) By separation of variables, derive two ordinary differential equations of r and w =cos e given by 12 F" (T) +2r F (r) - n(n + 1 ) Fr (r) = 0, (1 w2)G (w) - 2wG (w) + n(n+ 1)G, (w)...
Using this table determine the
van der Waal radius for Ar. Then use this radius to determine the
fraction of volume occupied by 1 mol of argon at 25C and 1 atm.
Table 17.2 Lennard-Jones Parameters for Atoms and Molecules Particle e/kJ mol-1 o/Å 0.997 1.77 0.307 0.765 0.943 3.40 4.10 2.93 3.92 3.65 4.33 3.82 1.65 1.23 2.02 C6H6 8.60
Fluid Mechanics
#1 Laminar Flow in Pipes The axial velocity in a pipe of radius R is given by, . Find the value of r (as a fraction of R) that maximizes u(r). How does this value of velocity compare with Vc? Compute the wall shear stress, du or Perform a control volume analysis on a pipe section of length e. Relate the pressure drop across the pipe section to the shear stress. Substitute the relation above for tw to...
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