Chemical Engineering Knowledge

Sherwood Number

The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of convective mass transport to diffusive mass transport.

It is defined as follows

\mathrm{Sh} = \frac{K L}{D} = \frac{\mbox{Convective mass transfer coefficient}}{\mbox{Diffusive mass transfer coefficient}}

where

L is a characteristic length (m)
D is mass diffusivity (m².s⁻¹)
K is the mass transfer coefficient (m.s⁻¹)

Using dimensional analysis, it can also be further defined as a function of the Reynold and Schmidt numbers:

\mathrm{Sh} = f(\mathrm{Re}, \mathrm{Sc})

Prandtl Number

The Prandtl number

\mathrm{Pr}

is a dimensionless number that is defined as the ratio of momentum diffusivity (kinematic viscocity) to thermal diffusivity.

It is defined as:

\mathrm{Pr} = \frac{\nu}{\alpha} = \frac{\mbox{viscous diffusion rate}}{\mbox{thermal diffusion rate}} = \frac{c_p \mu}{k}

where:

$\nu$ : kinematic viscocity, $\nu = \mu/\rho$ , (SI units : m²/s)
$\alpha$ : thermal diffusivity, $\alpha = k/(\rho c_p)$ , (SI units : m²/s)
$\mu$ : dynamic viscocity, (SI units : Pa s = N s/m²
$k$ : thermal conductivity, (SI units : W/(m K) )
$c_p$ : specific heat capacity, (SI units : J/(kg K) )
$\rho$ : density, (SI units : kg/m³ ).

Pr < 1 means thermal diffusivity dominates and Pr >1 means momentum diffusivity dominates.

Nusselt Number

Nusselt number is the ratio of convective heat transport to conductive heat transport normal to the fluid boundary. It is a dimensionless number used in heat transfer in boundary of fluid.

where,

h = heat transfer coefficient (Btu / hr.m2.K)

L = characteristic length (m) (see below)

k = thermal conductivity (Btu.m / hr.m2.K)

Nusselt no. greater than 1 shows that heat transfer by convection is dominant as compared to that by conduction. And Nusselt no. less than 1 shows the opposite.

Selection of the characteristic length should be in the direction of growth (or thickness) of the boundary layer; some examples of characteristic length are: the outer diameter of a cylinder in (external) cross flow (perpendicular to the cylinder axis), the length of a vertical plate undergoing natural convection, or the diameter of a sphere. For complex shapes, the length may be defined as the volume of the fluid body divided by the surface area.

Reynold's Number

Reynold's number is a dimensionless number and it is the ratio of "inertial forces" to "viscous forces" in the fluid. Interpreting it in physical terms, it tells about the nature of flow of the fluid i.e, it tells about whether the flow is turbulent, laminar or transition flow.

Mathermatically, Re = ρdv/µ = inertial forces / viscous forces.

Where, ρ = density of fluid (kg/m3)
d = diameter of pipe (m) = for non-circular pipes equivalent diameter is used
v = velocity of fluid (m/s)
µ = viscocity of fluid (kg/m.s)

If Re < 2000 , the flow is said to be laminar and if the Re > 3000, the flow would be turbulent one. Between this boundry, the flow is transitional.

Measure Capacity Of Pump Practically

Capacity of pump is the volume of liquid displaced per unit time. During running of pump you can measure it's capacity at any time. For this you need a pump, stop watch, a container of definite shape. Here is the procedure:

Method:
1) Start the pump and keep on running it for some time. Both the suction and discharge valves should be open.
2) Take a container of a definite shape so that you can measure it's volume. Lets take a cylindrical type basket whose dimensions is known.
3) Now, put the basket at the discharge end and at the same time start the stopwatch.
4) After some time (let's say 10 seconds) take the basket out of the liquid flow at discharge and at the same time stop the stopwatch.
5) Measure the volume of the filled liquid using V = πr²l ( l = height of the liquid in the basket)
6) Divide this volume by time.

That's it. Be careful about unit consistency.

Capacity Of Pump

Capacity of a pump is the amount of liquid that a pump can displace per unit of time. If a pump is transporting 12 gallons in one minute, then it's capacity is said to be 12 gallons per minute or 12 gpm.

Fromula:
Q = V/t
where,
Q = Capacity of pump
V = Volume of fluid
t = Time

Surging In Compressors and It's Effects On Compressor

Before understanding the surging process, you need to understand head and capacity concept of a compressor.

Maximum Head of Compressor:

Maximum head of the compressor is the head achieved when the compressor performs maximum amount of work on per mass of gas. This is practically achieved when operating the compressor at it's minimum capacity.

Minimum Capacity of Compressor:

When the pressure at the discharge vessel is quite low than the maximum head of compressor, the compressor will work at at maximum capacity and minimum work per mass of gas. When the discharge pressure starts increasing, the pump have to work more on per mass of gas and starts running on less capacity, until a minimum capacity and maximum head of compressor is achieved.

SURGING:

Suppose a compressor is connected to a system that needs a large amount of gas or is at very low pressure. The suction of the compressor is connected to the system having good enough pressure. You want to transfer the gas from high pressure vessel to the low pressure vessel. You start the compressor that starts transferring the gas from high pressure vessel to the low pressure vessel. Since at this stage, there is a little resistance of pressure at the discharge side of the compressor, the compressor capacity is high at start.

Transferring the gas continuously will increase the pressure continuously at the discharge vessel and hence the resistance to the discharge also increases. This happens if you are not using that gas at the same rate. The compressor capacity also starts decreasing continuously, since the compressor discharge pressure have to overcome that discharge vessel pressure in order to continue to transfer the gas. Hence compressor will have to use more power to work more on per mass of gas.

A stage will come when the pressure at the discharge vessel becomes higher than the maximum head of the compressor. The flow of gas stops i.e, the capacity of the compressor drops less than the minimum capacity and the gas will flow in reverse direction i.e, from discharge vessel towards the compressor. This suddenly decreases the pressure in the discharge vessel than the maximum head of the compressor. Therefore, the compressor again starts delivering the gas to the discharge vessel.

Gas pressure in the discharge vessel again becomes more than the maximum head of the compressor and the phenomenon of reverse flow and forward flow happens so on.

This rapid flow of gas back and forth in the compressor is called Surging. In other words, one can say that the surging occurs when the compressor is operated below it's minimum capacity.

Effects Of Surging On Compressor:

Surging sets up severe vibrations in compressor and associated piping which can cause damage to the compressor.

Wednesday, 8 October 2014