What is the domain of dependence?

Area outside the left running wave

Area within the downstream characteristics

Area within the upstream characteristics

Area which does not lie within the characteristic lines

Correct Answer : Area within the upstream characteristics

Explanation : If we consider a point A in the flow field through which two characteristic lines pass (C₊ and C_–) then area which is between the two upstream characteristics of both left and right running waves is known as domain of dependence.

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What is the region of influence?

Area outside right running wave

Area outside the left running wave

Area within the upstream characteristics

Area within the downstream characteristics

Correct Answer : Option (D) : Area within the downstream characteristics

Explanation : For a point A which is present in a flow field with incoming steady supersonic flow, there will be two characteristic lines passing through them. The area formed between these two characteristics in the downstream region is known as region of influence.

For a point in the supersonic flow lying at the intersection of the characteristics, its flow field properties depend on change in which of these regions?

Region of influence

Domain of dependence

Region outside the characteristics

Intersection points of the characteristics

Correct Answer : Option (B) : Domain of dependence

Explaination : If a point P lies at the intersection of the left and right running waves, the flow field properties at point P is dependent on the flow field information in the region upstream i.e. domain of dependence.

On which of these points does the properties of flow field at point A depend?

Point B

Point C

Point D

Point P

Correct Answer : Option (D) : Point P

Explaination : Point P lies at the intersection of the two characteristic lines. Point A lies in the region of influence thus its flow properties depend on the properties generated due to disturbances at point P which is the intersection point.