Measure Volume of Irregular Lamina - Using Screw Gauge

Introduction

Measuring volume of irregular lamina using screw gauge has many practical applications in our daily life. we observe many objects that are irregular in shape with different thicknesses. Measuring thickness, area, and volume parameters for regular smooth objects will be easy. But for irregular objects, these parameters need an instrument and carefully acquiring the values. Here, an irregular lamina object’s volume is measured by knowing the parameters area, and thickness of the lamina object.

What is Screw Gauge?

To measure the small values of physical parameters of irregularly shaped objects, we need an accurate instrument. “Screw Gauge” is an instrument, that helps in measuring the parameters like radius or thickness of a wire, metal sheet, a lamina, etc accurately. The thickness value from the screw gauge depends on the least count, pitch, and the number of rotations. The various parts of the screw gauge are shown in the diagram below:

Fig 1: Screw gauge construction.

Explain the least count.

The minimum value measured for the physical parameters by vernier callipers and screw gauge instruments is the Least Count.

$$\mathrm{Least\: count\: of\: a\: Scale=\frac{minimum\: reading\: of\: the\: scale }{Number\: of\: divisions\: on\: the\: scale}}$$

$$ \mathrm{=\frac{1mm}{1\: divisions}=1mm }$$

$$\mathrm{Least count of vernier calipers=\frac{minimum\: reading\: of\: the\: scale }{Number\: of\: divisions\: on\: the\: vernier\: scale}}$$

$$\mathrm{=\frac{1mm}{10\: divisions} = 0.1 mm}$$

What is irregular lamina?

Objects around us are flat and thin like leaves, flatbread, etc. These types of objects are called Lamina. Objects having a perfect shape and measurable physical parameters are regular lamina. Objects having irregular shapes need instruments to measure their physical parameters due to nearly negligible values at different points on their surface, such as irregular lamina.

Fig 2: Examples of the regular and irregular lamina.

Aim

To calculate the volume of an irregular lamina, by knowing its thickness using a Screw Gauge.

Material used

An irregular-shaped lamina, a Screw Gauge, pencil, and graph paper.

Theory

The formula for the volume of the irregular lamina

$$\mathrm{The\: volume\: of\: irregular\: lamina = area\: \times \: thickness}$$

Formulas for thickness using screw gauge

$$\mathrm{The\: pitch\: of \: screw\: gauge\: = \frac{distance\: that\: the\: screw\: moved }{Number\: of\: rotations}}$$

$$\mathrm{Least\: count\: of\: screw\: gauge\: = \frac{Pitch\: of\: screw\: gauge}{Number\: of\: divisions\: on\: the\: circular\: scale}}$$

The area is calculated using graph paper, by counting the number of squares that the irregular lamina boundary occupied.

Diagram

Procedure

• Take the graph paper of side length 1 cm and place the irregular lamina on it. With the help of a pencil outline the irregular lamina on graph paper.

• Count the number of full squares of the graph present inside the outline of the irregular lamina and note the value. Similarly, note down half squares within the outline, also considered full squares.

• Multiply the total number of squares with the area of one square of the graph. This gives the area of the irregular lamina.

• If the zero point on the circular head scale coincides with the zero point in the pitch scale, then the screw gauge has no zero error.

• Put the irregular lamina between the stud and screw by rotating the ratchet, until the stud, irregular lamina, and screw will contact each other tightly.

• Note down the value in the pitch scale which coincides with the circular scale just below the zero point in the circular scale. Note down the number of divisions in the circular scale that are beyond the zero point in the pitch scale.

• Repeat the process and note down the values three to five times, so that the average values are taken. Multiply each circular scale reading with the least count of screw gauge and add the value to the pitch scale reading.

Calculation

Let the distance moved by the screw be 0.5 mm and the number of rotations is 1. Then,

$$\mathrm{The\: pitch\: of\: screw\: gauge\: =\frac{0.5 mm }{1}=0.5 mm}$$

Let the number of divisions on the circular head scale be 50. Now the least count of screw gauge is

$$\mathrm{Least\: count\: of\: screw\: gauge\: =\frac{0.5 mm}{50} = 0.01 mm}$$

Let the average pitch scale value that coincides with the circular scale before the zero point be 2 mm, when the irregular lamina is placed. The average value of the number of divisions on the circular scale that coincides with the zero point on the pitch scale is 44.

Total thickness reading = [pitch scale value + (circular scale value) × least count]- zero correction.

= [2 mm + (44) × 0.01 mm] - 0 = 2.44mm

From figure 3, the number of full squares of graph paper is three and four half squared within the outline of the irregular lamina. There are five fully squared on the graph paper and the area of the squares is 1 cm².

Area of the irregular lamina = number of fully squared boxes × length of the square box =5 ×1 cm²=5cm²

Convert the thickness unit from mm to cm. Since 1 mm = 0.1 cm

2.44 mm = 0.244 cm

Hence, the volume of an irregular lamina is

$$\mathrm{The\: volume\: of\: irregular\: lamina = area\: \times \: thickness}$$

$$\mathrm{ = 5 cm^2 \times \: 0.244 cm}$$

\mathrm{= 1.22 cm^3}

Result

Physical parameters of the given irregular lamina are

Thickness = 0.244 cm.

Area = 5 cm^2.

Volume = 1.22 cm^3.

Source of error

• There can be a little source of human error while taking scale readings on the screw gauge.

• If their irregular lamina is not flat or plane fully, then there may be a source of error in thickness.

Conclusion

An irregular lamina’s volume is measured by finding its area and thickness of it. The area is calculated by using graph paper and counting the number of squares within the irregular lamina.

FAQs

1. What is the difference between Vernier calliper and screw gauge?

Vernier Callipers least count is 0.1 mm, while the least count of screw gauge is 0.01 mm. It means with a screw gauge we can measure the very small thickness compared to vernier callipers.

2. Write any two uses of screw gauge.

• A screw gauge is used in measuring the thickness of the uniform metal sheets and a glass slab.

• The radius or diameter of circular objects like wire can also be measured by a screw gauge.

3.What is zero positive error?

In the screw gauge without any object between the stud and screw, if the zero point on the circular scale is below the central line of the pitch scale, the zero error is positive.

4. What is zero negative error?

In the screw gauge without any object between the stud and screw, if the zero point on the circular scale is above the central line of the pitch scale, the zero error is negative.

5. What is back lash error?

While rotating the screw for taking readings, the screw may not be tight and it may slip due to the tear of threads, called a backlash error of screw.