Pressure In static Fluids Fluid Mechanics Pressure In static Fluids CHE 312/CHE315 Pressure In static Fluids

Objectives Define and classify fluids Define static Fluids vs. Dynamic Fluids Explain pressure in a static fluid Derive the equation of pressure in a static fluids Show examples of applications of static pressures. CHE 312/CHE315 Introduction

Fluid: A continuous substance whose molecules move freely past one another and that has the tendency to assume the shape of its container; a liquid or gas. CHE 312/CHE315 Introduction

Types of Fluids: Incompressible Fluids: Effect of pressure on the fluid is neglected (small). --------------------------------------------------------------------------------------------------------------------------------------------------- Most liquids are incompressible CHE 312/CHE315 Introduction

Gases are compressible Types of Fluids: Compressible Fluids ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Gases are compressible CHE 312/CHE315 Introduction

static Fluids vs. Dynamic Fluids CHE 312/CHE315 Introduction

Pressure in A Static Fluid Furnace duct Pipe or tube Dam Pressure is a Normal Force (acts perpendicular to surfaces) It is also called a Surface Force CHE 312/CHE315 Introduction

P=F/A P=rgh F =mg P = h ρ g + P0 Pressure in A Static Fluid P0 h P CHE 312/CHE315 Introduction

Pressure in A Static Fluid x z Z Force Balance SF =0 DZ Think-Pair-Share How many force components are making the balance? z+Dz P+DP z P ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- CHE 312/CHE315 Introduction

Pressure in A Static Fluid Fz+Dz Fz W Force Balance SF =0 z+Dz P+DP z P Fz =PA Fz+Dz = (P+DP)A W = mg =(rV)g =r(ADz)g Assumptions? dP+rgdz = 0 DP+rgDz = 0 CHE 312/CHE315 Introduction

the vertical height of a fluid that determines the pressure in fluid, the shape of the vessel does not affect the pressure. CHE 312/CHE315 Introduction

CHE 312/CHE315 Introduction

CHE 312/CHE315 Introduction

Introduction Related Links: http://www.youtube.com/watch?v=YlmRa-9zDF8&feature=related http://www.youtube.com/watch?v=UuK3ESGgbqk&NR=1 CHE 312/CHE315 Introduction

Summary ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- CHE 312/CHE315 Introduction

Pressure In static Fluids 2.2C Head of a fluid Pressures units: Pascal (N/m2), Psi, dynes/cm2, etc… A common method of expressing pressure, is in terms of head (h) in meter (m) or feet (ft) of a particular fluid: ……………………………………………………………………. …………………………………………………………………….. Example: Atmospheric Pressure? CHE 312/CHE315 Pressure In static Fluids

Pressure In static Fluids in SI units h (m) = P/(r*g) h (ft) = P*gc/(r*g) in English units ……………………………………………………………………. …………………………………………………………………….. Example: Atmospheric Pressure? CHE 312/CHE315 Pressure In static Fluids

Pressure In static Fluids 2.2D Devices to Measure Pressure and Pressure Differences In industrial processing, it is important to measure and control the pressure and/or the liquid level in a vessel or process. For Flowing pipes, flow rate is also needed. Thus, pressure measurements are important. CHE 312/CHE315 Pressure In static Fluids

Simple U-tube Manometer Pa Pb 4 2 3 1 5 ra rb R Z Density of Fluid A > Density of Fluid B A and B are immiscible Pa is exerted on one arm of the tube and Pb is exerted on the other arm. CHE 312/CHE315 Pressure In static Fluids

Pressure In static Fluids Pressure difference between Pa and Pb: Pressure at point 1: P1=Pa Pressure at point 5: P5=Pb At point 2: P2=Pa+(Z+R) rB g (R: reading of the manometer) Pa Pb 4 2 3 1 5 rA ra rb rB R Z CHE 312/CHE315 Pressure In static Fluids

Pressure In static Fluids At point 3: P3=P2 Also, P3= Pb+Z rB g + R rA g Therefore, P3= Pa+(Z+R) rB g = Pb+Z rB g + R rA g Pa Pb 4 2 3 1 5 rA ra rb rB R Z Pa -Pb= R (rA- rB) g (SI ) Pa -Pb= R (rA- rB) g/gC (English ) CHE 312/CHE315 Pressure In static Fluids