bw version ecw211 4 hydrostatic forces

7/29/2019 Bw Version Ecw211 4 Hydrostatic Forces

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Chapter 3:

Hydrostatic Forces


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Learning outcomes

By the end of this chapter students should be able to:

Understand hydrostatics concept and principles.

Able to calculate hydrostatic forces for plane,

inclined & curved surfaces and by pressure

diagrams.

Able to calculate centre of pressure for plane,

inclined & curved surfaces and by pressurediagrams.

UiTMKS/ FCE/ BCBidaun/ ECW211 2


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Introduction

Fluid statics deals with problems associated with fluid

at rest.

In fluid statics, there is no relative motion between

adjacent fluid layers. Therefore no shear stresses inthe fluid trying to deform it.

The only stress we deal with in fluid statics is the

normal stress i.e. pressure.

The force exerted on a fluid at rest is normal to the

surface at the point of contact.



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Introduction

Principles in hydrostatics:

There are no shear stresses.

The pressure exerted by a fluid under hydrostatics

condition at any depth is equal in all directions.

The pressure acts perpendicular to an immersed

surface.

Hydrostatic pressure varies linearly, increasingwith an increase in depth.



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Hydrostatic forces on plane surfaces



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Hydrostatic forces on plane surfaces

If the plane surface is horizontal as in figure above, the

pressure anywhere on the plane surface is given by,

The resultant force,

Where

= mass density of fluid

A = surface areah = depth from free water surface

g = gravity acceleration


ghp

gAh

pAF


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Example 3.1

A rectangular tank 6 m and 3 m wide contains water up to a

depth of 2.5 m. Calculate the pressure and resultant hydrostatic

force on the base of the tank.


6 m

3 m

2.5 m

kN

ApF

Pa

ghp

45.441

3624525

24525

5.29810


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Hydrostatic forces on inclined surfaces


GgAhF

G

G

GP h

Ah

Ih

2sin


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Geometrical properties of common figures



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Example 3.2

An inclined rectangular gate, 1.5 m by 1.0 m with water on

one side is shown in Fig 3.3. Determine the total resultant

force acting on the gate and locate its centre of pressure.



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Example 3.3

A circular butterfly gate pivoted about a horizontal axis passing through its

centroid is subjected to hydrostatic thrust on one side and counterbalanced

by a force F, applied at the bottom as shown in Fig. 3.4 If the diameter of

the gate is 4 m and the water depth is 2 m above the gate, determine the

force F required to keep the gate in position.



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Example 3.4 (Bansal, 2003)

A rectangular plane surface is 2 m wide and 3 m deep. It lies invertical plane in water. Determine the resultant force and

position of centre of pressure on the plane surface when its

upper edge is horizontal and (a) coincides with water surface,

(b)2.5 m below free surface.



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Example 3.5 (Douglas, 2006) A trapezoidal opening in the vertical wall of a tank is closed by a flat plate

which is hinged at its upper edge (as shown in figure). The plate is

symmetrical about its centreline and is 1.5 m deep. Its upper edge is 2.7 m

long and its lower edge is 1.2 m long. The free surface of the water in the

tank stands 1.1 m above the upper edge of the plate. Calculate the moment

about the hinge line required to keep the gate close.



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Example 3.6 (Bansal, 2003)

A circular plate 3.0 m diameter with a concentric circular hole of 1.5 m

diameter is immersed in water in such a way that its greatest and least depth

below the free surface are 4 m and 1.5 m respectively. Determine the

resultant force on one face of the plate and the position of the centre of

pressure.



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Example 3.7

A triangular plate is

immersed in a liquid of

specific gravity 0.85.

The plate has a circularhole with a diameter of

1.0 m. Determine the

total force in kN acting

on the plane. Locate thecentre of pressure.


2 m

0.6 m

1 m

4 m


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Pressure diagram


h1

h2

gh1

gh2

gh1

h1

h2

gh2

h


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Another method to determine hydrostatic force & CP.

General principal:

Hydrostatic force per unit width of immersed

surface is given by the area of the pressure

diagram.

The FR is given by the volume of pressure prism.

CP is given by the location of the centroid pressure

diagram.



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Example 3.12

A 2 m x 3 m tank with vertical sides contains

oil of density 900 kg/m3 to a depth of 0.8 m,

which floats on 1.2 m depth of water as shown

in figure. Calculate the resultant hydrostaticforce and its location on the 3 m side of the

tank.



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Example 3.13 (Douglas, 2006)

A closed tank, rectangular in

plan with the vertical sides,

is 1.8 m deep and contains

water to a depth of 1.2 m.

Air is pumped into the spaceabove the water until the air

pressure is 35 kNm-2 . If the

length of one wall of the

tank is 3 m, determine theresultant force on this wall

and the height of the centre

of pressure above the base.



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Suhaimi 3.1

A tank shown in Fig. is

filled with oil (SG 0.8) and

water to a depth of 10 and

6 metres respectively.Using the method of

pressure diagram, find the

resultant force from all

fluids acting on the gate of1.8 m by 9 m.

Ans:494.424 kN



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Suhaimi 3.3

An inclined plane surfac is

submerged in liquid of

specific weight . If the

width of the surface is bfind a general expression

for the resultant force F

and the centre of pressure

h.



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Suhaimi 3.4

The gate shown in Fig. is 2 m wide and 6 mlong, hinged at point B. If the weight of the gate

is 10000 kg, determine the force in the bar AD.

Ans: 102.748 kN



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Suhaimin 3.6

A door 0.7 m by 1.6 m high hinged at A, separates oil

and water as shown in Fig. The left side has 1.6 m of

oil (SG 1.5) while the right side contains 0.9 m of

water. Calculate the force P (magnitude and direction)required to keep the door close?

Ans: 9.333 kN/m



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Review of past semesters final

exam questions

bw version ecw211 4 hydrostatic forces

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