# Hydrostatics and Properties of Fluids Lab Report

Categories: Physics

### Introduction

The Hydrostatic Bench is intended for the demonstration of the fluid's hydrostatic characteristics and behavior (fluid at rest). This enables learners to acquire a comprehension of a variety of basic concepts and methods before they study liquids in motion[1].

### Theoretical Background of Experiment

#### 2.1 Density

The density of any liquid is characterized as the mass per unit volume and is signified by 'ρ'. It ought to be noticed that the density of a fluid remains reasonably consistent because the volume involved by a given mass of fluid is practically constant.

However, gases are compressible, and their density changes with volume[1].

#### 2.2 Capillarity

Capillarity refers to the rise or fall of liquid levels in small cavity tubes, depending on the angle of contact between the fluid and the tube surface. For fluids that wet the tube, a rise occurs, while for fluids that don't wet the tube, a depression results. Surface tension (σ) supports the gravitational force on the raised liquid column in capillary tubes, affecting pressure measurements[1].

#### 2.3 Hydrostatic Pressure

Hydrostatic pressure is the pressure applied by a liquid at rest at a given point within the liquid due to gravity. It increases with depth from the liquid surface. In a container, the depth of an object submerged in the liquid can be measured, and the pressure experienced by the object depends on the liquid's density and depth above it[2].

#### 2.4 Viscosity

Viscosity, represented by the Greek symbol 'μ' (mu), is a measure of a liquid's resistance to flow due to shearing stress within the liquid.

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It is defined as the ratio of shearing pressure 'τ' to the rate of change of velocity 'v'. Viscosity calculations may vary for laminar and turbulent flow, determined by the Reynolds number of the flowing liquid. Laminar flow occurs at Reynolds numbers below 2300[3].

### Application in Industry

Hydrostatic testing is widely used in industry to check the integrity of pressure vessels, such as boilers, tubes, and cylinders, for leakage or defects. It ensures the safety and quality of pressure vessels operating under pressure conditions. Hydrostatic testing is crucial for identifying leaks in low-pressure devices like pipes and plumbing systems. Additionally, it can be used to verify burst and proof pressures[4].

### Experimental Setup

#### 4.1 Equipment

The experimental apparatus consists of a comprehensive bench equipped with all necessary equipment for conducting hydrostatics and properties of fluids experiments. Some equipment is rigidly mounted on the bench, while others are suitable for use on the bench top. The bench includes a water reservoir for experiments requiring a free-water surface, and a drainage system for collecting and returning water to the reservoir. Equipment for determining fluid properties includes a Eureka can, a specific gravity bottle, a hydrometer, a capillarity apparatus, a falling-disc viscometer, and a vernier angle gauge for liquid level measurement[5].

#### 4.2 Setup

The experimental procedure involves several steps for different measurements:

1. Determining the density of a fluid by measuring the mass of an empty beaker, filling it with the liquid, and calculating the density.
2. Measuring the density of an object using the Eureka can method.
3. Conducting Bourdon Pressure Gauge experiments to determine pressure changes under varying conditions.
4. Investigating capillarity by observing liquid rise in tubes with different diameters.
5. Determining the viscosity of two different fluids using a viscosimeter and calculating kinematic and dynamic viscosity[6].

### Experimental Data and Analysis

#### 5.1 Density of Liquids and Solids

• Mass of empty beaker: m = 46.1 g
• Volume of filled beaker with fluid: v = 40 ml
• Mass of filled beaker: m = 86.99 g
• Density of fluid: ρ = 1020 kg/m³
• Object weight: m = 180.8 g
• Weight of empty beaker: m = 46.1 g
• Weight of filled beaker: m = 111 g
• Calculated density of object = 2785.8 kg/m³

#### 5.2 Bourdon Pressure Gauge Data

Mass added to piston (kg) Total mass with piston M (kg) Actual Pressure p (kN/m²) Gauge reading (kN/m²) - Increasing Pressure Gauge error (kN/m²) Gauge reading (kN/m²) - Decreasing Pressure Gauge error (kN/m²)
0.5 1 47 63 16 (34%) 56 9 (19%)
1 2 62 80 18 (29%) 76 14 (23%)
2 3 94 115 21 (22%) 112 18 (19%)
3 4 125 126 1 (0.8%) 150 25 (20%)
4 5 156 175 19 (12%) 175 19 (12%)

#### 5.3 Capillarity Data

Diameter of tube (mm) Height (ht) in mm Calculated Surface Tension (σ) in kg/s²
1.6 7 0.0274
0.8 12 0.0239
0.4 23 0.0225

#### 5.4 Viscosity Data

Dynamic viscosity:

• Distance: 200 mm
• Diameter: 1.6 mm
• Velocity of water: 10 m/s
• Velocity of oil: 0.7 m/s

Viscosity of water:

• μ₁ = 9.5×10⁻⁷ m²/s
• μ₂ = 9.5×10⁻⁷ m²/s

Viscosity of oil:

• μ₁ = 1.5×10⁻⁵ m²/s
• μ₂ = 1.39×10⁻⁴ m²/s

### Summary/Conclusions

In conclusion, this experiment conducted on the Hydrostatic Bench allowed us to study various aspects of hydrostatics and properties of fluids, including the density of liquids and solids, viscosity of different liquids, effects of capillarity, and Bourdon pressure gauge behavior. These experiments provide a solid foundation for understanding fundamental principles and behaviors of fluids at rest, which is essential before studying the motion of fluids[6].

Updated: Jan 05, 2024