FLUID MECAHNICS

HOME TASK ASSIGNMENT-1

Abstract:

In this home task, we have to find the density of the half-filled water container, the density of the can, then the density of the system (density of water + density of can). It is group work assigned to us. This basic purpose of this assignment is to well-known of the practical and research work. It also helps us to know the formal way of writing our research work. It also tells us about the density variation from the theoretical values and the reasons of this variations.

Introduction:

In this home task we have to find three things;

The density of the half-filled water (tap water) pot. (?w)

The density of the can. (?c)

The density of the system. (?s=?w+?c)

Density:

It is the defined as the mass per unit volume.

OR

It is the degree of compactness of a substance. 1

Mathematically;

Density (?) = Mass (m) / Volume (V)

Dependence:

Density is material property and depends on the material until physical conditions are same, it depends on two physical factors such as;

Temperature

Pressure

It is independent of the shape and geometry of the substance.

Density of water:

The Density of distilled water is same as that of pure water as it does not contain any impurities or salt content in it. The density of distilled water is 1 g/cm3, 1 kg per liter, 1 tone per m3 or one gram per ml.

The Density of tap water is 1 gram/cm3 and 1 gram per milliliter. It should be noted that mostly all the densities are the same. They differ in only points but the approximate values are used in calculations. 2

Methods and Materials:

Material:

I have used the aluminum oil container (olive oil) which is an alloy element coated.it contains of specifically two aluminum alloys;

Al-3004, which is used to make the body of the can.

Al-5182, which is used to make the lid of the can.

The density of the pure aluminum is 2700 kg/m3. However, its alloy 3xxx series has the density ranges from 2720-2511 kg/m3. 3

And the tap water is used in the experiment.

For the experiment the lid was removed.

Figure 1 Aluminum Alloys 4

Apparatus:

Electronic balance

Steel rule

Millimeter scale

Methods:

There are various methods to calculate the density of the material as;

Pycnometer method

Digital density meter

Refractometer; use to measure the density of crystals.

Hydrometer method

By knowing the mass and volume, and using the relation; ? = m/V

Experiment and Procedure:

Firstly, we will determine the mass of the empty can with the help of the electronic balance, and then we will tear the mass of can and add water in the can and we will determine the mass of the water used in the experiment too. The water is filled up to half of the can height.

Secondly, we have to calculate the volume of the can, which is the volume of hollow cylinder. So, using the formula for volume of hollow cylinder;

V = ?h (r12-r22)

where r1 and r2 are the internal and external radius of the can respectively. For calculating the density of the can (?c), divide the mass of the can by this volume.

Now, for calculating the volume of the water we will use the internal radius of the can, the height of the can and then using the half of the volume we obtain;

V = (?r22h)/2

For calculating the density of the water (?w), we will divide the mass of the water by this volume.

Finally, the volume of the whole system (?s=?w+?c) is calculated by adding the above two volumes, and then the density of whole system is calculated by the division of whole mass of system (mass of can and mass of the water) by the volume calculated now.

Calculations:

Outer radius of can = r1 = 4.45 cm = 0.0445 m.

Inner radius of can = r2 = 4.32 cm = 0.0432 m

Height of the can = h = 39.95 cm = 0.3995 m.

Height of the water in the can = h/2 = 19.97 cm = 0.1997 m.

Volume of the can = Vc = ?h (r12-r22) = 1.4310×10-4 m3.

Volume of the water = Vw = ?h (r12-r22)= 2.52×10-4 m3.

Volume of the whole system = Vs = ?h (r12-r22) + ?h (r12-r22) = 3.951×10-4 m3.

Mass of empty can = mc = 0.408 kg

Mass of water in the can = mw = 0.2492 kg

Mass of can half filled with water = ms = 0.6572 kg

Figures:

(Figure 2: Aluminum can half-filled with water)

Result:

Density of can = (?c) = mc/Vc = 2851.1 kg/m3

(Error from pure aluminum density = 5.59%)

Density of water = (?w) = mw/Vw = 996.7 kg/m3

(Error from density of pure water = 0.33%)

Density of whole system = ?s = ms/Vs = 1663.4 kg/m3

Assumptions and Approximations:

The curved sides of cylinder were considered smooth regardless of the small pits.

At the top of the can there was bulging outside material with greater thickness, for the experiment it was assumed to be perfectly cylindrical shape.

The can was roughly filled half, it was assumed that it is precisely the half of the original volume of can.

Discussion:

The volume of the can was calculated with taking the thickness of walls in consideration as well. It was thus considered a hollow cylinder.

The volume of the whole system was calculated in 2 steps, the lower half as a solid cylinder of water, cylinder base and cylinder walls and the upper half as a hollow cylinder.

The aluminum was not pure rather it was the alloy with the metal manganese. This type of aluminum alloys falls in 3xxx series. Which are greatly malleably, and their temperature coefficient make their use in oil cans.

Another reason, to some extent, for error in aluminum density might be our assumption of can as a uniform cylinder and neglecting the outward projection on top of the pot, made for holding purposes.

Conclusion:

This experiment helps us to know how practically we can find the density of the materials in our daily life to check the purity of the material. It also develops our skills to do the practical work confidential. It also helps us to do work in groups. Moreover, it develops our curiosity for finding the new information and builds the professional way of writing the research report.

Reference:

1. https://www.bing.com/search?q=density&qs=n&form=QBRE&sp=-1&pq=density&sc=8-7&sk=&cvid=500B452142D941B5AFA9371DC4842092

2. https://www.bing.com/search?q=density%20of%20water&qs=n&form=QBRE&sp=-1&ghc=1&pq=density%20of%20water&sc=8-16&sk=&cvid=82DE52A6DDDB485196A43442E326BEEB

3. https://en.wikipedia.org/wiki/Aluminium_alloy

4. https://www.bing.com/images/search?q=aluminum+alloys+table&FORM=HDRSC2\