2.0 FLUID PRESSURE

2.1 Pressure and pressure variation in a fluid at rest.
The pressure indicates the normal force per unit area at a given point acting on a given plane. Since there is no shearing stresses present in a fluid at rest - the pressure in a fluid is independent of direction. For fluids - liquids or gases - at rest the pressure gradient in the vertical direction depends only on the specific weight of the fluid. Direction of the pressure-induced forces in a fluid at rest because fluids deform continuously when exposed to any shear stress at all, the only force that can be applied to a surface in a fluid at rest must be normal to that surface.

Thus, as a (real or imaginary) surface is moved in any direction in a fluid, the force on it shifts to always remain perpendicular to every part of the surface. Fluid at rest is no shear stresses and only normal forces due to pressure

2.1.1 Concept of pressure and pressure head

Intensity is the amount of atmospheric pressure and the weight of the fluid at a unit area at one point or surface. Usually the pressure intensity referred to as pressure only.

The pressure at depth h is γh
Pressure, P = γh kN/m2
= ρgh ………………………………………………..( 3.1) where h is measured in vertical

Pressure in water is proportional to the depth in the fluid may be indicated by a triangle as in diagram above. If there is a small body in the fluid does not move, pressure must be the same intensity in all directions to maintain the value of equilibrium. Lines of action of pressure forces must perpendicular to any surface of the body. Any two points at the top the same horizontal plane must have the same pressure.

Example 2.1
A working diver 18m below sea level. Calculate the pressure suffered due to the water column. (specific weight of water = 10,000 N/m3)

Solution: -

P = ωh kN/m2
= 10,000 X 18
= ...

-1.293 0 0.23 0.3 0.307 0.6 0.69 0.75 000 000n/m2 062 1 1.0 1.293 10 10.34 10.35 100 1000 1000x9.81 1000x9.81x6 101.325 103 123606h 13.6 133416h 18 180kn/m2 18m 1m 2 2.0 2.1 2.1.1 2.1.2 2.1.3 2.1.4 2.1.5 2.1.6 2.10 2.2 2.3 2.4 2.5 2.6 2.65 2.7 2.8 2.9 2256.3 23cm 2943 2m 3 3.1 30 30cm 34.06 340 35 353.54 35x103 37943 4.503 4503 5.9 600mm 66.708 66708 6768.9 6867 69cm 6m 750mm 760 760mm 769mmhg 8.752 800kg/m3 800x9.81x1 9.81 9810 9810h 9810x absolut act action actual air also altitud alway amount appli approxim area arm atmospher b baromet barometr base bodi bottom calcul call caus center chang circumst close cm column concept contain continu d datum deform densiti depend depth determin diagram differ differenti direct distribut diver draw due earth either elev empti enhanc equal equilibrium equival everi exampl exert expos figur flow fluid follow forc gage gase gaug gh gh2 given gradient h h1 h2 h3 head height hg high horizont hydrostat ii iii imaginari independ indic induc instal intens iv kg/m3 kn kn/m2 left less level line liquid listen locat loss low m m2 maintain manomet mass may measur mercuri mm move much must n n/m2 n/m3 negat neglig normal note occur oil one p p1 pa pab pair part patm per perfect perpendicular pg pgage pgh1 pgh3 phonet pic piezomet pipe plane pm pn point posit present presser pressur pressure-induc properti proport provid pw r read real reduc reduct refer relat relationship remain rest right rise sea see shear shift shown simpl sinc small solut space specif standard stress suffer surfac surround tank therefor thus top triangl true tube two type u u-tub understand unit use usual v vacuum valu variat vertic wall water weight wherea work x z zero ª ªzª ªæªçªèªéªêªëªíªîªïªðªñª ç ì þþþöö γh ρ ρ1g1h1 ρ2g2h2 ρa ρag ρagh1 ρg ρgh ρgh1 ρgx ρr ρrgh2 ρugh1 ρw ρwg ρwgh1 ωh