H11 Apparatus

SECTION 1.0 INTRODUCTION

Figure 1 H11 Apparatus

The TQ H11 Centre of Pressure Apparatus permits the moment due to the fluid thrust on a wholly or partially submerged plane surface to be measured directly and compared with theoretical analysis. Provision is made for varying the inclination of the plane surface subjected to the fluid pressure so that the general case may be studied.

1.1 Description of Apparatus

Water is contained in a quadrant of a semi-circular Perspex tank assembly which is allowed to swing on a smooth bar.

The cylindrical sides of the quadrant have their axes coincident with the centre of rotation of the tank assembly, and

therefore the total fluid pressure acting on these surfaces exerts no moment about that centre. The only moment present

is that due to the fluid pressure acting on the plane surface. This moment is measured experimentally by applying weights

to a weight hanger mounted on the opposite side to the quadrant tank.

A second tank, situated on the same side of the assembly as the weight hanger, provides a trimming facility and enables

different angles of balance to be achieved.

The angular position of the plane and the height of water above it are measured on an angular scale engraved on the tank

and a linear scale on the back panel.

Included with the apparatus are base leveling feet and a spirit level.

1.2 Installation and Preparation

With the quadrant tank of the hopper fabrication held to the right-hand side, fit the hopper fabrication onto the centre

support of the main frame assembly.

Level the base plate by screwing the adjustable feet and observing the spirit level.

A colored dye is supplied with the apparatus, which can be added to the water to help observation during

experimentation. It should only be necessary to add small amounts of dye (one or two capfuls) to produce suitable

coloring.

The apparatus should be cleaned regularly using soapy water. When cleaning, care should be taken to ensure that no

traces of grit or any hard abrasive materials are present on the cloth used. Do not use any materials containing man-made

fibers as these will scratch the Perspex.

SECTION 2.0 THEORY

2.1 Definition of Centre of Pressure

Centre of pressure may be defined as the point in a plane at which the total fluid thrust can be said to be acting normal

to that plane.

2.2 Analysis

Figure 2 Schematic of Centre of Pressure Apparatus

The following analysis applies to the condition of a plane surface at various angles when it is wholly or partially

submerged in a fluid.

Let breadth of quadrant = B

and weight per unit volume = ω

Referring to Figure 2, consider an element at start depth y, width oy.

Force on element of = ω(y cosθ - h)Bdy

and the Moment of Force on element about 0 = ωB(y cosθ - h)yδy

Therefore, total moment about 0 = M = ω B ∫(cosθy2 - hy)dy

Case 1: Plane Fully Submerged

Limits R1 and R2

This equation is of the form of y = mx + c. A plot of M against h will yield a straight line graph of gradient

. The value of ω can now be calculated.

Case 2: Plane Partially Submerged

Limits R2 and h secθ

Hence:

Rearranging:

ω can be obtained from Case I and h3 can then be plotted against

SECTION 3.0 EXPERIMENTAL PROCEDURE

Set up the equipment as previously described in Section 1.2, and affix the weight hanger to the hanger support located

on the top left of the hopper. The apparatus will now require trimming in order to bring the submerged plane to the

vertical (i.e. 0° position). This is achieved by gently pouring water into the trim tank until the desired position is achieved.

The horizontal line on the tank assembly should be read against 'the zero line on the back scale.

Add a 20 g weight to the weight hanger. Pour water, with dye added if necessary, into the quadrant tank until a 0° balance

is restored. Note the weight and the height reading of the water (h). Repeat the procedure for the full range of weights.

Empty both tanks of water. Again, with the weight hanger alone in position, trim the assembly by gently adding water

to the trim tank until a 30° balance is achieved. Add a 20 g weight, restore balance to 30° point and record values for h

for the full range of weights.

Readings may be tabulated in the form outlined in Table 1 and the results calculated in line with the theory given in

Section 2.

Table 1 Format of results

Figures 3 and 4 show the general form of the graphs expected from this

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