# ENGR2000 Lecture Notes - Lecture 2: American Broadcasting Company, Ya Sin, Sluice

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2nd-Year Fluid Mechanics, Faculty of Science & Engineering, Curtin University

ENGR2000: FLUID MECHANICS

For Second-year Chemical, Petroleum, Civil & Mechanical Engineering

FLUID MECHANICS LECTURE NOTES

CHAPTER 2: HYDROSTATICS

This chapter is concerned with the eﬀect of ﬂuids when ﬂow is absent - hence

the name hydro(water∗1)-statics(forces balanced - hence, no acceleration). In

hydrostatics it is the gravitational forces on the bulk of ﬂuid that create the

pressure in the ﬂuid; in a later chapter we will see that ﬂuid ﬂow aﬀects this

pressure.

Hydrostatics is very important in Engineering because the hydrostatic forces

in ﬂuids can create large forces that act on structures - for example the ﬂuid

force on a dam due to the reservoir that it holds. A knowledge of these forces

then permits the appropriate design of the structure upon which they act.

We will also see that hydrostatic forces are essentially responsible for the

capability of objects, such as ships, to ﬂoat in a ﬂuid medium. (And, hot-air

balloons to ﬂoat in air.) This aspect of hydrostatics is called buoyancy and

its fundamentals are covered in this chapter.

2.1 Hydrostatic pressure

We ﬁrst wish to quantify hydrostatic pressure in a ﬂuid. We know that, for

example, a scuba diver experiences increasing pressure the deeper that s/he

dives. The simple reason for this is that the deeper s/he goes, the greater the

weight of water there is above him applying a force (per unit area) to his/her

body. This type of approach leads us to derive an expression for hydrostatic

pressure.

Consider a tank of ﬂuid which contains a very thin plate of (neutrally buoy-

ant) material with area A. This situation is shown in Fig. 2.1a. If the plate

1∗However, many of the principles also apply to gases - the discipline is so called because

the ﬂuid forces are very large for liquids which have a high density as compared to gases

which have relatively low densities.

Chapter 2 −Page 1

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2nd-Year Fluid Mechanics, Faculty of Science & Engineering, Curtin University

is in equilibrium (it does not start to move), then the forces on it must be

balanced. On the top side of the plate acts the weight of the ﬂuid, with den-

sity ρ, above it in the downward direction. Because it does not accelerate,

there must be a force acting upwards on the underside of the plate - this is

the eﬀect of the hydrostatic pressure acting on the plate.

FIGURE 2.1: (a) Thin plate in a ﬂuid, (b) Free-body diagram for the plate

The weight of the ﬂuid above the plate is

FW= density ×volume of ﬂuid above ×g

=ρg(Ah) (2.1)

Balancing this is the hydrostatic pressure, p, acting over the area, A, of the

underside of the plate depicted in Fig 2b. Balancing the two forces yields

pA =ρgAh

cancelling Agives the expression for the hydrostatic pressure as

p=ρgh in N/m2or Pa (Pascals) (2.2)

noting that his the vertical depth. You can now see the relationship between

hydrostatic pressure and gravitational forces. We have derived Eqn. 2.2 for

a particular depth, h. We could derive it for any depth, y, where yis a

downward coordinate from the liquid surface, giving the formula p=ρgy.

Chapter 2 −Page 2

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2nd-Year Fluid Mechanics, Faculty of Science & Engineering, Curtin University

We now note that this pressure is the same at all points in the ﬂuid with the

same vertical location (y-coordinate)) for an interconnected body of ﬂuid.

To illustrate this, lines of constant pressure are shown in Fig. 2.2.; i.e. a

plot of p=ρgy for diﬀerent values of y. The resulting diagram represents

the pressure ﬁeld in the ﬂuid. Note that these lines are all horizontal

because there is no variation with the horizontal coordinate, x, in the pressure

formula.

FIGURE 2.2: The pressure ﬁeld in an interconnected body of static ﬂuid

If we evaluated the expression above, we would not ﬁnd the total pressure

acting on the plate. This is because, using the same arguments, there is a

column of atmospheric air above the water in the tank and this presses down

on the water which, in turn, transmits the additional pressure onto the plate

. If we denote the air pressure at the liquid surface PA(again, in N/m2),

then the total pressure at a depth his

pabs =ρgh +PA(2.3)

This is called the absolute pressure whilst the pressure of Eqn. 2.2 is called

the gauge pressure, i.e. the pressure relative to atmospheric pressure.

In the derivation above, we can also see that the downward force on the

upper side of the plate also has an intensity, or pressure, given by ρgh. In

fact the eﬀect of the ﬂuid loading above results in a hydrostatic pressure,

acting downwards, on the upper side of the plate.

So far, it seems that pressure only acts in the vertical direction. We now show

that at any point in the ﬂuid, the same pressure actually acts in a direction

Chapter 2 −Page 3

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