Vishwakarma Government Engineering College

FLUID MECHANICS -2

Presentation on {FLUID MECHANIS}

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NAME ENROLLMENT

1 Shukla Meet 1401701190562 Sindhi Parth 1401701190573 Soni Kunjan 1401701190584 Thakar Chetan 1401701190595 Thakar Milan 140170119060

Free Surface of Water

• A horizontal surface upon which the pressure is constant every where.

• Free surface of water in a vessel may be subjected to:

- atmospheric pressure (open vessel) or, - any other pressure that is exerted in the vessel

(closed vessel).

• Atmospheric pressure is approximately equal to a 10.33-m-high column of water at sea level.

• Any object located below the water surface is subjected to a pressure greater than the atmospheric pressure (P > Patm).Let:

dA = cross-sectional area of the prism. the prism is at rest. So, all forces acting upon it must be in equilibrium in all directions.

Absolute and Gage Pressures

Notice that:• If the two points are on the same elevation, h =

0 PA=PB

• In other words, for water at rest, the pressure at all points in a horizontal plane is the same.

Equilibrium in x- direction: Fx = PA dA – PB dA + g L dA sin q = 0

PB – PA = g h The difference in pressure between any two points in still water is always equal to: the product of the specific weight of water (g) and the difference in elevation between the two points (h).

Pressure gages: are usually designed to measure pressures above or below the atmospheric pressure.

Gage pressure: is the pressure measured with respect to

atmospheric pressure (using atmospheric pressure as a base).

Absolute pressure: Pabs = Pgage + Patm

Pressure head, h = P/g

If the water body has a free surface that is exposed to atmospheric pressure, Patm. Point A is positioned on the free surface such that PA= Patm

(PB )abs= PA + g h = Patm + g h = absolute pressure

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Notice that:• Any change in pressure at point B would cause an equal change at point

A, because the difference in pressure head between the two points must remain constant = h.

Pascal's law : A pressure applied at any point in a liquid at rest is transmitted

equally and undiminished in all directions to every other point in the liquid.

This principle has been made use of in the hydraulic jacks that lift heavy weights by applying relatively small forces.

The difference in pressure heads at two points in water at rest is always equal to the difference in elevation between the two points.

(PB /g) – (PA /g) = D(h)

A manometer Is a tube bent in the form of a U containing a fluid of known specific

gravity. The difference in elevations of the liquid surfaces under pressure indicates the difference in pressure at the two ends.

Two types of manometers:

1. An open manometer: has one end open to atmospheric pressure and is capable of measuring the gage pressure in a vessel.

2. A differential manometer: connects each end to a different pressure vessel and is capable of measuring the pressure difference between the two vessels.

Manometers

• The liquid used in a manometer is usually heavier than the fluids to be measured. It must not mix with the adjacent liquids (i.e., immiscible liquids).

• The most used liquids are: - Mercury (specific gravity = 13.6), - Water (sp. gr. = 1.00), - Alcohol (sp. gr. = 0.9), and - Other commercial manometer oils of various

specific gravities.

A simple step-by-step procedure for pressure computation

Step1: Make a sketch of the manometer system approximately to scale.

Step 2: Draw a horizontal line at the level of the lower surface of the manometer liquid, M. The pressure at points 1 and 2 must be the same since the system is in static equilibrium.

Step 3: a) For open manometers P2 = P1

gM.h = gW.y + PA

PA = gM.h - gW.y

12A simple step-by-step procedure for pressure computation

b) For a differential manometers P2 = P1

gM.h + gw .(y - h) + PB = gW.y + PA

DP = PA – PB = h (gM - gw )

Buoyancy

• When a body is submerged or floating in a static fluid, the resultant force exerted on it by the fluid is called the buoyancy force.

• The buoyant force has a magnitude equal to the weight of the fluid displaced by the body and is directed vertically upward.

• This force will act vertically upward through the centroid of the volume of fluid displaced, known as the centre of buoyancy.

Archimedes' Principle

The weight of a submerged body is reduced by an amount equal to the weight of the liquid displaced by the body.

BodybyDisplacedFluidb VF g

Buoyancy of a submerged body

dAhhVF BodybyDisplacedFluidV )( 12 gg

• The stability of a floating body is determined by the relative positions of the center of gravity of body G and the center of buoyancy B.

• The body is in equilibrium if: - W must equal Fb (buoyancy force) - G and B lie on the same vertical line.

Flotation Stability

• When the body is displaced through an angle q , the center of buoyancy move from B to B` and a turning moment is produced.

• M (metacentre) is the point at which the line of action of the upthrust Fb intersects the vertical line through G.

• GM known as the metacentric height.

• Then:q GMW generatedMoment

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