CHE213 Fluid Mechanics UITM Assignment Sample Malaysia

CHE213 Fluid Mechanics is an exciting course offered by Universiti Teknologi MARA (UITM). In this course, we will delve into the fascinating world of fluid dynamics, exploring the behaviour and properties of liquids and gases. Fluid mechanics is a fundamental branch of engineering and physics that plays a vital role in various industries, such as aerospace, civil, mechanical, and chemical engineering.

Throughout this course, we will explore the principles and laws governing fluid flow, including fluid statics, fluid kinematics, and fluid dynamics. We will delve into topics such as fluid properties, fluid forces, fluid flow measurement, and analysis of fluid systems. By studying these concepts, you will gain a deep understanding of how fluids behave and the principles that govern their motion.

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In this segment, we will provide some assignment briefs. These are:

Assignment Brief 1: Ability to explain and solve problems related to fluid properties as well as pressure force; apply dimensional analysis to develop a relationship between fluid variables.

Fluid properties and pressure forces are important concepts in the study of fluid mechanics. Let’s start by understanding these terms and then apply dimensional analysis to develop a relationship between fluid variables.

Fluid Properties: Fluids are substances that can flow and conform to the shape of their container. The properties of fluids include density, viscosity, pressure, and temperature.

  1. Density: Density (ρ) is the mass per unit volume of a fluid. It determines the fluid’s resistance to acceleration or deceleration. The SI unit of density is kilograms per cubic meter (kg/m³).
  2. Viscosity: Viscosity (μ) is a measure of a fluid’s resistance to flow. It determines the fluid’s internal friction. Viscosity can be classified as either dynamic viscosity or kinematic viscosity. Dynamic viscosity (η) is the ratio of the shearing stress to the velocity gradient in a fluid. Kinematic viscosity (ν) is the ratio of dynamic viscosity to density. The SI unit of dynamic viscosity is pascal-second (Pa·s) or poise (P), while kinematic viscosity is measured in square meters per second (m²/s).

Pressure Force: Pressure (P) is defined as the force exerted per unit area. It is the perpendicular force exerted by a fluid on a surface, resulting from the collisions of fluid particles. The SI unit of pressure is pascal (Pa), which is equal to one newton per square meter (N/m²).

Pressure force (F) can be calculated using the formula: F = P × A where F is the pressure force, P is the pressure, and A is the area on which the pressure acts.

Dimensional Analysis: Dimensional analysis is a technique used to relate physical quantities by their dimensions. It helps in understanding the relationship between various fluid variables without detailed mathematical calculations.

To apply dimensional analysis, we need to identify the relevant variables and their dimensions. Let’s consider a scenario where we want to find a relationship between pressure (P), velocity (V), density (ρ), and a characteristic length (L).

The dimensions of the variables are: [P] = [Force/Area] = [M][L][T]⁻² [V] = [L][T]⁻¹ [ρ] = [M][L]⁻³ [L] = [L]

We can express these dimensions as powers of fundamental dimensions: [M] = M¹ [L] = L¹ [T] = T¹

Now, let’s find the relationship between these variables using dimensional analysis. We can express pressure force (F) as a function of the other variables:

F = P × A = P × L²

Since [F] = [M][L][T]⁻² and [L] = L¹, the dimensions on both sides must be equal. Therefore, we can write:

[M][L][T]⁻² = [P][L]²

Substituting the dimensions in terms of fundamental dimensions:

(M¹)(L¹)(T¹)⁻² = (M¹)(L¹)(T⁻²)(L²)

By comparing the powers of M, L, and T on both sides of the equation, we get:

1 = 1 0 = 2 -2 = 0

The last equation tells us that there is no direct relationship between time (T) and the other variables in this scenario.

Hence, based on dimensional analysis, the relationship between pressure (P), velocity (V), density (ρ), and characteristic length (L) can be represented as:

P = k × ρ^a × V^b × L^c

where k is a dimensionless constant and a, b, and c are exponents determined by experimental data or theoretical analysis.

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Assignment Brief 2: Ability to explain types of fluid flow,define and derive continuity and Bernoulli’s equations and their applications in flow metres, notches and weirs.

Fluid flow refers to the motion of a fluid, such as a liquid or gas, through a channel or pipe. There are different types of fluid flow, characterized by the behavior and characteristics of the fluid as it moves. The main types of fluid flow include laminar flow, turbulent flow, and transitional flow.

  1. Laminar Flow: Laminar flow occurs when a fluid moves in smooth, parallel layers with minimal mixing between them. The fluid particles move in a regular and predictable manner. Laminar flow is characterized by low velocities and a high degree of order. The flow is typically steady, and the fluid particles follow well-defined paths. Laminar flow is common in small pipes or channels with low flow rates and high viscosity fluids.
  2. Turbulent Flow: Turbulent flow is the opposite of laminar flow and is characterized by chaotic, irregular motion of fluid particles. In turbulent flow, the fluid particles mix vigorously, resulting in eddies, swirls, and fluctuations in velocity and pressure. Turbulent flow is often observed at high velocities or in large pipes and channels. It is less predictable and more challenging to analyze than laminar flow.
  3. Transitional Flow: Transitional flow is an intermediate state between laminar and turbulent flow. It exhibits some characteristics of both laminar and turbulent flow, depending on the flow conditions. As the flow rate or other factors change, transitional flow can transition from laminar to turbulent or vice versa.

Now, let’s move on to the continuity equation and Bernoulli’s equation, which are fundamental principles used to analyze fluid flow.

Continuity Equation: The continuity equation is based on the principle of conservation of mass. It states that the mass flow rate of a fluid is constant within an incompressible flow system. The equation is derived from the concept that the mass entering a given section of a pipe or channel must be equal to the mass exiting that section.

The continuity equation can be expressed mathematically as follows: A₁V₁ = A₂V₂

Where: A₁ and A₂ are the cross-sectional areas of the pipe or channel at two different points. V₁ and V₂ are the velocities of the fluid at the respective cross-sectional areas.

This equation implies that as the cross-sectional area of a pipe decreases, the fluid velocity increases, and vice versa, in order to maintain a constant mass flow rate.

Bernoulli’s Equation: Bernoulli’s equation relates the pressure, velocity, and elevation of a fluid along a streamline. It is based on the principle of conservation of energy for a flowing fluid.

The Bernoulli’s equation can be expressed mathematically as follows: P₁ + ½ρV₁² + ρgh₁ = P₂ + ½ρV₂² + ρgh₂

Where: P₁ and P₂ are the pressures at two different points along the streamline. ρ is the density of the fluid. V₁ and V₂ are the velocities of the fluid at the respective points. g is the acceleration due to gravity. h₁ and h₂ are the elevations of the fluid at the respective points.

Bernoulli’s equation suggests that as the fluid speed increases, the pressure decreases, and vice versa. It provides insights into the relationship between fluid velocity, pressure, and elevation in different flow situations.

Applications in Flow Metres, Notches, and Weirs: Flow metres, notches, and weirs are devices used to measure or control the flow of fluids. The continuity equation and Bernoulli’s equation play a crucial role in their operation.

Flow metres are instruments that measure the volume or mass flow rate of a fluid. They utilise principles such as the continuity equation to relate the fluid velocity and cross-sectional area to calculate the flow rate.

Notches and weirs are types of flow measurement devices that utilise the principles of fluid flow to determine the flow rate. They consist of a specially shaped opening or obstruction in a channel through which the fluid flows. By measuring the height of the fluid above the notch or weir and applying Bernoulli’s equation, the flow rate can be determined.

Assignment Brief 3: Ability to apply appropriate equations and principles to analyse a variety of flow characteristics in circular pipes; explain pump performance characteristics and Net Positive Suction Head (NPSH).

Flow Characteristics in Circular Pipes: When analyzing flow characteristics in circular pipes, several equations and principles are commonly applied. Here are some key concepts:

  1. Continuity Equation: The continuity equation states that the mass flow rate of a fluid remains constant along a pipe. It can be expressed as A1V1 = A2V2, where A1 and A2 are the cross-sectional areas of the pipe at two different points, and V1 and V2 are the corresponding velocities.
  2. Bernoulli’s Equation: Bernoulli’s equation relates the pressure, velocity, and elevation of a fluid along a streamline. It can be written as P1 + 0.5ρV1^2 + ρgh1 = P2 + 0.5ρV2^2 + ρgh2, where P1 and P2 are the pressures, V1 and V2 are the velocities, ρ is the fluid density, g is the acceleration due to gravity, and h1 and h2 are the elevations at two different points.
  3. Darcy-Weisbach Equation: The Darcy-Weisbach equation is used to calculate the head loss in a pipe due to friction. It can be expressed as hL = f(L/D)(V^2/2g), where hL is the head loss, L is the pipe length, D is the pipe diameter, V is the velocity, f is the Darcy friction factor, and g is the acceleration due to gravity.

Pump Performance Characteristics: Pump performance characteristics describe the relationship between flow rate, head, and power in a pump. Key characteristics include:

  1. Pump Curve: The pump curve is a graphical representation of the pump’s performance. It shows the relationship between flow rate (Q) and total dynamic head (H) at different operating points.
  2. Head-Flow Curve: The head-flow curve indicates how the pump’s head varies with different flow rates. It helps determine the pump’s ability to generate pressure at different operating conditions.
  3. Efficiency Curve: The efficiency curve represents the pump’s efficiency at various flow rates. It helps determine the point of maximum efficiency for a given pump.

Net Positive Suction Head (NPSH): Net Positive Suction Head (NPSH) is a measure of the pressure available at the inlet of a pump to prevent cavitation. Cavitation occurs when the pressure at the pump inlet drops below the vapor pressure of the fluid, causing the formation of vapor bubbles and subsequent damage to the pump.

NPSH consists of two components:

  1. NPSH Available (NPSHa): NPSHa is the measure of the absolute pressure at the pump suction inlet. It includes the pressure from the fluid’s surface, pressure due to elevation, and any additional pressure provided by a booster pump or other equipment.
  2. NPSH Required (NPSHr): NPSHr is the minimum pressure required at the pump inlet to avoid cavitation. It depends on the pump design and can be obtained from the pump manufacturer’s data.

To ensure proper pump operation and avoid cavitation, the NPSHa must be greater than the NPSHr. If the NPSHa is too low, cavitation can occur, leading to reduced pump performance, increased noise, and potential damage.

Understanding the flow characteristics in circular pipes and pump performance characteristics, along with considering NPSH, is crucial in designing and analyzing fluid flow systems.

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