CE 230-Engineering Fluid Mechanics Week 2 Pressure Variation in Static Fluids & its Applications

What can we say about the pressure at a point in a static fluid? Consider equilibrium of the shown element

Conclusion Only normal forces exist in static fluid Pressure at a point in a static fluid is independent of direction

Pressure variation in a static fluid

Relation between gage and absolute pressure

Pressure variation in a static fluid

This equation is valid as long as we are in the same fluid. Pressure difference between two points in a static fluid is the weight of unit fluid column between them dp/dz = -γ z +ve up This equation is valid as long as we are in the same fluid. Two possibilities Constant γ Variable γ

What is the pressure at a depth of 35 ft in the tank?

What is the pressure at the bottom of the tank? S(oil)=0.8

Problem 3.16 What is the maximum pressure in the odd tank?

Manometry Use of pressure change with elevation to determine pressure at a point Use of pressure change with elevation to determine the difference in pressure between two points

Problem 3.30 Find pressure at pipe B.

Problem 3.39 Find pressure at pipe A.

Problem 3. 31 If the air is under atm. P. the water position is 1 Problem 3.31 If the air is under atm. P. the water position is 1. Find P if l=40 cm. Dia ratio=8, density = 800 kg/m3

Determine the weight of the man if the piston weighs 50 lb and area in contact with water is 1.5 ft2

Problem 3.42 determine the difference in pressure between points A and B.

What if γ is variable? (Compressible fluid) For air say γ = pg/RT in troposphere T=T0-α(z-z0) Integrate basic equation to get pressure variation

Figure 3. 5 (p. 39) Temperature variation with altitude for the U. S Figure 3.5 (p. 39) Temperature variation with altitude for the U.S. standard atmosphere in July (2).