STATIC PRESSURE

 INTRODUCTION 

Fluid statics is concerned with fluid at rest.  A fluid is said to be at rest when it is completely free from shear stress and hence all forces due to a static pressure must act at right angles to the containing surface. 

With a static fluid, the only physical factor concerned is gravity.  Accordingly, the free surface of the fluid will always be horizontal and, therefore, the intensity of pressure on any horizontal plane within the body of the fluid will be the same. 

EXPERIMENT  

FREE SURFACE OF STATIC LIQUID 

Object 

To show that the free surfaces of a static liquid is horizontal. 

Apparatus 

See diagram below.   This apparatus is attached to the Armfield Hydrostatic Work Bench. 
(See photograph on Lab experiment page)

 Analysis 

From what you were told in the introduction, the only physical factor involved with a static fluid is gravity, so the free surface will always be horizontal. 

Method 

(a)        Make sure valves V3 and V4 are closed 

(b)       Open valves V1, V2 and V5.  V5 is located at the top of tube ‘a’ 

(c)        Using the hand pump located adjacent to the small sink, transfer water from tank 1, below   the work bench, into tank 2 until the level coincides with the first horizontal line on the tank      wall. 

(d)       Note that the level in each of the three tubes, "a", "b" and "c", is the same and in line with the first horizontal line on the tank.  

(e)        Repeat for the second, third and fourth horizontal lines noting that the level of the water is always horizontal, irrespective of tube size or shape. 

(f)        Drain the water from tank 2 by opening valve V3 and re-establish the level at the first horizontal line. 

(g)       Close valve V3 and ensure that valve V1 is open.  Close valve V5 at the top of tube "a" (tube "a" no longer has a free surface exposed to atmospheric pressure).

 (h)              Using the hand pump, transfer water from tank 1 into tank 2 again.  Raise the level in tank 1 to the second, third and fourth horizontal lines.  Note that the level in tube "a" remains depressed whilst "b" and "c" follow the level in the tank as (e).

Experiment 

EFFECT OF FLOW ON FREE SURFACE 

Object 

To study the effect of flow on the free surface. 

Apparatus 

As for previous experiment. 

Analysis 

Consider energies above datum at the free surface in tank 2 and at a point ‘u’

Note:  All dimensions must be in metres. 

The Potential energy at the free surface of tank 2 above datum = h 

Energy at ‘u’ is made up of:           pressure energy    metres 

                                                            Kinetic energy       metres 

From the law of conservation of energy, since energy cannot be created or destroyed, 

As you will recognise from your lecture notes, this is the basis of the Bernoulli Equation 

Losses may be expressed as a function of  and you will be using the D’Arcy Equation to explore these losses. 

When the fluid is at rest, v = 0 and  will be equal to h which you established in the previous experiment. 

When the fluid moves, v will be greater than zero and thus  will now be equal to h₁ which is actually equal to h – y as shown on the apparatus diagram.  The value of y is thus a function of velocity squared. (v²) 

Method 

(a)               Ensure that valves V3 and V4 are closed

(b)               Open valves V1, V2 and V5

(c)               Using the hand-pump, transfer water from tank 1 into tank 2 until the level coincides with the fourth horizontal line.

(d)              Open valve V3 so that the water flows from the system to the drain.  Make sure that the level in tank 2 remains as constant as possible by operating the hand pump.

(e)               Observe that the level in tubes ‘a’, ‘b’ and ‘c’ fall below the level in tank 2.  This loss in head corresponds to the friction in the moving liquid.  All three tubes should indicate the same level since they are connected to the same point in the system with no flow between them.

(f)                 Close valve V3 and open valve V4 so that water flows along the interconnecting pipe-work to the drain.  Make sure that the level in tank 2 remains constant by operating the hand pump.

(g)               Observe that the levels in tubes ‘a’, ‘b’ and ‘c’ are progressively lower than the level in tank 2.  This is due to the fact that the movement of the liquid along the interconnecting pipe results in frictional losses between the vertical tubes.  Loss between the tubes ‘a’ and ‘b’ is small compared with the loss between ‘b’ and ‘c’.  Why is this the case?

 Return to Lab experiments

Home