Mathematics Homework Solutions

Volume Calculation: Fluid into a box

How many fluid mls would fit into a box measuring 3626mm in lenth, 1875mm in width and 1216mm in height?

Mass Balance Problem

See attached for full problem. The concentration of isobutene in the overhead product is 4.8 mole %, and the concentration of propane in the bottoms is 0.7 mole %. Calculate the moles of the various components in the overhead and bottoms per 100 moles of feed.

Show a velocity expression satisfies the given partial differential equation.

Thank you in advance for your help in solving this problem. See attached problem statement.

Boundary Conditions

In solving transport phenomena problems, we use "boundary conditions" and "initial conditions". In mathematical terms, (that is, types of variables), what are "boundary conditions" and what are "initial conditions"

Differential equations - 2 Water tanks

Two identical water tanks labeled A and B are resting at the same elevation and are linked via a pipe with a valve. The cross sectional area of each of the tanks is 1m^2. The valve demonstrates linear behavior (volumetric flow is linear with pressure drop) and will allow a flow of 0.5 m^3/min under a pressure drop equivalent to ...continues

Gradients : Conservation of Mass in Equivalent Form.

Show that the equation of conservation of mass {see attached} can be written in the equivalent form {see attached} where {see attached} denotes the material derivative of the flow.

Gradients : Summation Identities

Please see the attached file for the fully formatted problems.

Find the Acceleration Field

If the velocity field of a flow is given by {see attached} where {see attached} and Q is a positive constant, show that {see attached} everywhere except at the origin. Find the acceleration field. *See attachment for figures and equations.

Streamlines : Find particle paths in parametric form.

If {see attached} where {see attached} are positive constants, calculate the streamlines and find the equations of the particle paths in parametric form.

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