Question

List all different types of mass conservation (continuity) equations we discussed
throughout the semester in lectures. Discuss their applicability, limitations and assumptions
used for their derivation.

Answer 1

The congruity condition mirrors the way that mass is monitored in any non-atomic continuum mechanics investigation. The condition is created by including the rate at which mass is streaming all through a control volume, and setting the net in-stream equivalent to the pace of progress of mass inside it.

Mass preservation conditions are utilized to show the compartment's conduct. The law of protection of mass is seen in a fair concoction condition, which is a synthetic condition that shows all mass is preserved all through the response. In a reasonable concoction condition, the number and sorts of molecules on each side of the condition ought to be equivalent .

Coherence guideline : What streams into a characterized volume in a characterized time, short what streams out of that volume in that time, must collect in that volume. The standard is a result of the law of protection of mass.

The progression condition is characterized as the result of cross sectional territory of the funnel and the speed of the liquid at some random point along the channel is consistent.

The congruity condition is the announcement of protection of mass in the pipeline: mass in short mass out equivalents change of mass. The primary term in the condition "mass stream in short mass stream out "of a cut of the pipeline cross-segment.

As per the coherence condition, a liquid willl go progressively quick through the limited piece of the pipe.The stream speed is higher in the choked piece of the channel. The more extensive the funnel is, the more slow is the stream speed, if the channel limits, the stream speed will increment.

The coherence condition in liquid elements portrays that in any consistent state process, the rate at which mass leaves the framework is equivalent to the rate at which mass enters a framework.

u = Flow speed vector field.

The progression condition applies to all liquids, compressible and incompressible stream, Newtonian and non-Newtonian liquids. It communicates the law of preservation of mass at each point in a liquid and should thusly be fulfilled at each point in a stream field.

The congruity condition is significant for portraying the development of liquids as they go from a container of more prominent width to one of littler breadth. It is basic to remember that the liquid must be of consistent thickness just as being incompressible .

Since fluids are incompressible, the pace of stream into a region must approach the pace of stream out of a region. This is known as the condition of coherence. The condition of progression can show how much the speed of a fluid increments in the event that it is compelled to move through a littler territory.

One-dimensional conduit indicating control volume. Presently we apply the guideline of mass protection. This is an announcement of the rule of mass preservation for a consistent, one-dimensional stream, with one delta and one outlet. This condition is known as the congruity condition for consistent one-dimensional stream.

Congruity condition is nonstop, implying that you can get speed at a throat with ceaselessly changing thickness. For the pitot tube, be that as it may, straightforward mass preservation will work - this is fundamentally coherence in an alternate structure. For a pitot tube, the progression condition isn't required on the grounds that the speed at the passage to the pitot tube is known, to be specific zero.

This condition is known as the congruity condition for consistent one-dimensional stream. For a consistent course through a control volume with numerous gulfs and outlets, the net mass stream must be zero, where inflows are negative and outpourings are sure.

Suspicion of Continuity Equation The cylinder is having a solitary section and single exit. The liquid streaming in the cylinder is non-gooey. The stream is incompressible. The liquid stream is consistent.