Month: April 2016

Hydrostatics

Hydrostatics

Hydrostatics                  04/25/16

 

Hydrostatics is the study of the physics and applications of incompressible fluids at rest in stable equilibrium. The weight of a fluid displaced in water can be expressed symbolically as F=*V*g, where is the fluid density (assumed to be constant) Vis the volume, and g is gravity of the planet. The pressure on a liquid submerged in a fluid can be calculated at P= gh+P0, where Pis the pressure his the vertical displacement and P0is the atmospheric pressure (or the pressure at the top of the fluid surface). The study of hydrostatics is of fundamental importance to the field of Mechanical Engineering

Environmental stress cracking

Environmental stress cracking

   Environmental stress cracking                 04/24/16

 

One of the most common unexpected brittle failures of all thermoplastic materials is environmental stress cracking. ESC occurs when polymers are exposed to liquid chemicals that accelerate the crazing process, which results in cracking at pressures below standard air temperature. The study of ESC has application within the automobile industry, where the need to keep polymers stable is paramount

Brittleness

Brittleness

Brittleness          04/23/16

 

An object is considered brittle if it breaks from stress without significant deformation. Such an object requires little energy to be broken. The brittle strength of an object can be increased by subjecting it to pressure.

Thermoplastics

Thermoplastics

Thermoplastics         

        04/22/16

 

Thermoplastics are plastic materials that become pliable once a certain temperature threshold has been reached and revert back to being rigid once cooled to a certain temperature. The amorphous nature of thermoplastics are less susceptible to chemical attacks and environmental stress cracking due to lacking such a clearly defined structure. Teflon is an example of an application of thermoplastics

Solving first order systems using matrices

Solving first order systems using matrices

      Solving first order systems using matrices               04/21/16

 

Suppose we have a first order system with equations x(t)’ =ax(t)+by(t)and y(t)’=cx(t)+dy(t). We can solve these equation by putting the equations into a matrix form. The matrix will end up with a, b, c, and din progressing order. By taking the determinant, we can find the eigenvalues. We then transform this in to what looks like a solution to a second order differential equation C1*e1t*V1+C2*e2t*V2. We then solve for x(t)and y(t), with the front and bottom rows for the vectors are correlated with the x(t)and y(t)respectfully.

Auxiliary view

Auxiliary view

Auxiliary view                          04/20/16

 

When doing Mechanical Engineering design, many parts often have slanted platforms. These platforms usually become distorted when created using the standard top-front-right views, so Auxillary views were created in response. Auxiliary views take a snapshot of the object from a viewpoint that is centered on the slanted object. This makes it so the object is much easier to visualize. Often, a partial auxillary view is often used so only the important details of the slant are seen (much of the non slanted slide of the part is often unnecessary and becomes distorted itself when viewed through the auxiliary view).

Vector Field Diagrams

Vector Field Diagrams

Vector Field Diagrams          04/19/16

 

A most intuitive way of geometrically representing a solution of equations is through the use of a Vector field Diagram. To construct a vector field diagram, take two sets of equations dxdt=f(x,y)and dydt=g(x,y), set them equal to zero, and then isolate the xand y values on opposite sides. These sets of equations will determine the series of ordered pairs in which the slope is zero (in the horizontal or vertical direction for the f(x,y)and g(x,y) functions respectively). If one wants to see when the values are greater or less than zero, set the functions to a constant c greater than 0, and then solve with yas an isolate. These new solutions will determine the new slope in the x or y directions. One must combine the horizontal and tangential slopes to make the final value