PHY183-Lecture43 - Review Pressure The pressure at a given depth in a liquid is given by Physics for Scientists Engineers 1 Spring Semester 2006

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April 10, 2006 1 Engineers 1 Engineers 1 Spring Semester 2006 Lecture 43 April 10, 2006 2 Review - Pressure Review - Pressure ! The pressure at a given depth in a liquid is given by ! The gauge pressure is defined as the pressure difference relative to atmospheric pressure p = p 0 + ! gh April 10, 2006 3 Barometric Altitude Relation for Gases Barometric Altitude Relation for Gases ! In the derivation of the depth pressure relationship, we have made use of the incompressibility of liquids. ! However, if our fluid is a gas, we cannot make this assumption. ! We start again with a thin layer of fluid in a fluid column. ! The pressure difference between bottom and top surface is still given by the weight of the thin layer of fluid divided by the area " p = # mg A = # $ Vg A = # ( " hA ) g A = # g " h April 10, 2006 4 Barometric Altitude Relation for Gases (2) Barometric Altitude Relation for Gases (2) ! The negative sign indicates pressure decreases with increasing altitude ! So far nothing is different from the derivation of the incompressible case ! However, for compressible fluids we find that the density is proportional to the pressure ! Strictly, this relationship is only true for ideal gasses 0 = p p 0
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April 10, 2006 5 Barometric Altitude Relation for Gases (3) Barometric Altitude Relation for Gases (3) ! Combining our two equations gives us ! Taking the limit of ! h ! 0, we find the equation ! This equation is a differential equation, which has the solution ! This equation is known as the barometric pressure formula ! Assumptions: Ideal gas temperature does not change with altitude gravitation is constant ! p ! h = " g # 0 p 0 p dp dh = ! g
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This note was uploaded on 03/19/2008 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture43 - Review Pressure The pressure at a given depth in a liquid is given by Physics for Scientists Engineers 1 Spring Semester 2006

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