Process Calculation: Unit change in a formula

Fluid Flow: Bernoulli's theorem

Bernoulli's theorem is based on the principle of conservation of energy. In a flow of ideal fluid, we consider three types of energies on a macroscopic level, Potential Energy due to height from a reference point, Kinetic Energy due to velocity of fluid, Pressure Energy due to forces applied on the fluid. In Bernoulli's theorem three heads Potential head (z), kinetic head [(v^2)/2g] and pressure head (p/gρ). The total energy at every point in the flow is constant. the easy way to remember this equation is with the help of dimensions like [P/gρ =  (v^2)/2g = z ] have the same dimensions of length.

For a horizontal pipe flow, potential head is constant. the change in velocity head is converted into pressure head, which is the principle behind the flow meters.

As the area decreases pressure decreases according to Bernoulli's theorem but according to hydro-static law pressure is inversely proportional to area. In Bernoulli's theorem the pressure is hydrodynamic that means fluid is in motion. in this case, if area decreases velocity increases which results in decrease in pressure.

Mechanical Operation: Classification and Elutriation

The mixture of particles can be separated according to their settling velocity. the settling velocity for a system depends on diameter and density of particles. For two different types of materials having density difference can be separated into 3 fraction. one containing fine particles of lighter material, one containing coarse particles of heavier material and one having mixture of both as shown in figure.

In elutriation, a water stream is passed up to the column through bottom. the particles having settling velocity less than that of water velocity will be carried over and particles having larger settling velocity will be settled. to separate the mixture into more than 2 fraction, 2 or more elutriators can be connected in series with increasing area to reduce the water velocity.

The density of fluid can be taken in between the two fluids. for example in a mixture of quartz and galena with densities 2650 and 7500 kg/m3, if the fluid has density 2650 then quartz particle will have zero settling velocity and galena particles will settle down. But for a given size range we can calculate the minimum density of the fluid that can separate the particles. to find minimum fluid density we can equate the settling velocity for largest particle of lighter particle and settling velocity of smallest particle for heaviest particle. the density of fluid slightly greater than this will separate the particles. 

Mechanical Operation: Separation of Particles

The separation of particles is done on the bases of their properties, like size of the particle, density of particle. If the particles are of different sizes, then the separation can be done by either using screening or on the basis of difference between their settling velocities called sizing, and materials of same equivalent size are separated according to their densities called sorting.

because of size of particle and its density, particle will have different settling velocity, on the basis of which particles can be separated using a fluid whose density may be closer to one of the type of particles. the mixture of two types of materials A and B having same size range but different density, can be separated into 3 section consisting pure A, pure B and mixture of A and B.

   

Reverse Osmosis

Reverse osmosis is a phenomena used to get pure water. It is based on the reversal of the phenomena of osmosis. When a semi-permeable membrane (permeable for water) is placed between salt water and fresh water, water will start moving in direction of salt water, trying to equalize the concentration on both sides. This a natural phenomena, called osmosis resulting in dilution of concentrated solution. This process continues until the chemical potential becomes equal on both sides. The chemical potential of water in pure form is higher than that on the salt water side at same pressure. As water moves towards salted water, the pressure increases, which increases the chemical potential on that side. After some time the pressure reaches at a level at which the chemical potential on both sides becomes equal and the osmosis stops. Now the system is at equilibrium.

At osmotic equilibrium, at the same level, the pressure becomes P1 in the left and reaches P2 in the right. At this condition the chemical potential becomes equal. The difference in pressure is called osmotic pressure, and in order to get pure water (left side) a pressure greater than P2 has to be applied on the right (salt) side.  

Mechanical Operation: Size of an irregular particle

The size of of a sphere is taken in terms of diameter, but how can we determine the size of an irregular particle like gravels. The size of an irregular particle is taken as an equivalent diameter of a sphere. there are various basis on which the equivalent (nominal) diameter  is calculated. the basis of calculation depends on the application we use.
1. The largest dimension of the particle
2. The diameter of a sphere having
a) equal surface area of the particle like in adsorption, catalytic reaction
b) equal volume of particle like in fluid flow past immersed bodies, settling.
c) equal surface/volume of particle like gas liquid interface as in gas bubble
d) the same settling velocity as the particle
3. the size of the mesh screen like in crushing, grinding