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is pressure the same as stress ?

Stress is merely related to physical or mental tension which may be a result of pressure exerted to a material or a person. So pressure may cause stress and is not the same.

Pressure drop is the same as differential pressure as normally applied to measure the condition of a filter system.

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Not it is not

The more scientific definitions are:-

Pressure: compressive force acting on an area, expressed in units of force per unit of area, e.g. 1Pascal = 1 newton/metre (force) per square metre (area).

Pressure differential: change Differential to the more grammatically and mathematically correct Difference and there's the definition - difference between two pressures in a system.

Stress: force acting on an area, as above, but may be compressive or tensile.

Psychological stress is another matter, and most speakers use the word "stress" without knowing its proper meaning when talking of personal problems.

Strain: the change in shape of a medium under stress; e.g. compression of rubber or a gas, or the change in length of a spring under load.

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