MEC2404: Energy Laboratory Mechanics of Fluids

Assessment

The risk assessment for this laboratory can be found in SARAH, RA 24757. All students attending laboratory sessions on-campus are required to familiarize themselves with this document and follow the protocols/safe work instructions within it.

Introduction

This laboratory session will use a range of working sections to break down and teach the concepts of the Energy equation and implement them in practice. The Energy Equation is similar to Beroulli’s equation but incorporates terms to account for viscous losses (h_l) and energy added to the flow (h_g). 

Equation 1

Energy equation where is the pressure (Pa), is the fluid density (kg/m³), V is the velocity (m/s), is the gravitational acceleration (m/s²), is the height above a reference point (m), h_l is the head loss (m) and h_g is the head gain (m).

Another useful equation is the Continuity Equation which describes that the mass of the system must remain constant over time and since this system is a closed loop of water, the total flow rate will remain the same within the flow loop.

Equation 2

Continuity equation where is the fluid density (kg/m³), A is the cross-sectional area and V is the area normal flow velocity (m/s) 

The experimental apparatus offers the ability to measure pressures at various points in the flow. Pressure losses will occur throughout the system due to viscous effects (flow disturbance, flow separation, friction etc.). These losses can be categorized as major or minor losses.

Major losses occur due to viscous effects in straight sections of pipe (note we will assume that the flexible tubing used in this laboratory can be approximated as straight). The pressure head loss in a constant diameter section due to major losses is given by the Darcy-Weisbach equation:

Equation 3

Darcy-Weisbach major loss equation where h_{L major} is the pressure head loss (m), f is the dimensionless friction factor, L is the length over which the loss occurs (m), D is the diameter (m), V is the velocity (m/s) and g is gravity.

The friction factor f can be calculated from the Colebrook equation or read from a Moody chart and is a function of the dimensionless parameters Reynolds number Re_D and relative surface roughness of the pipe e/D.

Minor losses occur due to components of the system that disturb the flow e.g. valves, elbows, T-pieces etc. The flow through these components is complex. Rather than attempting to calculate the losses theoretically the pressure loss is described using an empirical loss coefficient. The pressure head loss due to minor losses in an individual component is given by:

Pre-Lab Questions

The results for these pre-lab questions should be entered into an online quiz which will close 10minutes before the start of the first Energy lab regardless of your allocated lab time.

1. Flow either side of a t-piece is shown in Figure 1. All flows are in the horizontal plane. Pitot tube flow meters with pressure measurements are fitted to two of the branches (top and RHS) while the other branch (LHS) has a sudden flow contraction. Pressures are measured at 4 points (labelled 1-4). The loss coefficient of the contraction connector K_L,cc is known but the loss coefficient of the T-piece K_L,TP is not. The known values are given in Table 2. In your calculations use 1000 kg/m³ as the density of water.

Calculate the following (you may assume major losses are negligible):

1. The velocities in the flow meters V₁ and V₃
2. The velocity after the contraction V_A
3. The loss coefficient of the T-piece K_L,TP (hint consider the flow between p₁ and p₃) where K_L,TP is based on the outlet velocity
4. The pressure after the contraction p_A

2. Flow either side of a t-piece is shown in Figure 2. All flows are in the horizontal plane. A pressure tapping gives the pressure of the flow coming into the left side of the T-piece. The known values are given in Table 3. In your calculations use 1000 kg/m³ as the density of water.

Summary of Assessment Requirements

The assessment focuses on applying fluid mechanics principles in a laboratory setting, specifically using the Energy Equation and Continuity Equation to analyze flow in a closed water system. Students are required to:

1. Understand and apply theoretical concepts:

   • Energy Equation: accounting for pressure, velocity, height, viscous losses (hl), and energy added to the system (hg).
   • Continuity Equation: mass conservation in a closed loop.
   • Major losses: via Darcy-Weisbach equation.
   • Minor losses: using empirical loss coefficients for valves, elbows, T-pieces, etc.

2. Complete pre-lab calculations:

   • Calculate velocities at various points in the flow system.
   • Determine loss coefficients for specific components (e.g., T-pieces).
   • Compute pressures after flow disturbances or contractions.

3. Follow lab safety and risk protocols:

   • Familiarize with SARAH RA 24757 and adhere to safe work instructions.

4. Demonstrate practical lab skills:

   • Measure pressures at multiple points.
   • Apply theoretical equations to real flow measurements.
   • Compare calculated and observed data.

Step-by-Step Academic Mentor Guidance

The Academic mentor guided the student through the assessment in a structured process:

1. Pre-Lab Preparation

• Objective: Ensure the student understands the theory and can perform preliminary calculations before entering the lab.
• Mentor Approach:
  • Reviewed the Energy and Continuity equations and their physical meanings.
  • Explained major vs. minor losses, introducing the Darcy-Weisbach equation and empirical loss coefficients.
  • Guided the student in interpreting T-piece and contraction configurations for pre-lab calculations.
  • Provided examples of calculating velocities (V1, V3, VA) and pressures (pA) using given densities and coefficients.

2. Understanding Loss Coefficients

• Objective: Apply theory to components affecting flow.
• Mentor Approach:
  • Explained the use of loss coefficients KL for T-pieces and contractions.
  • Demonstrated how to calculate unknown KL values using measured pressures and velocities.
  • Showed step-by-step derivation for the flow between p1 and p3 in a T-piece scenario.

3. In-Lab Implementation

• Objective: Perform measurements and validate theoretical calculations.
• Mentor Approach:
  • Demonstrated proper setup of Pitot tube flow meters.
  • Explained accurate reading of pressures at labeled points.
  • Guided the student in measuring velocities and comparing results with pre-lab predictions.
  • Ensured adherence to safety protocols from SARAH RA 24757.

4. Data Analysis and Verification

• Objective: Analyze and interpret experimental data.
• Mentor Approach:
  • Assisted in calculating velocity after contraction and pressure drop.
  • Guided in comparing theoretical vs. experimental values to understand discrepancies (e.g., minor unaccounted losses).
  • Encouraged the student to critically evaluate results and document findings.

Outcome Achieved

• Accurate pre-lab calculations: Velocities, pressures, and loss coefficients correctly determined.
• Practical application of theory: Energy and Continuity equations effectively applied to the closed-loop water system.
• Understanding of flow behavior: Student gained insights into major and minor losses, and how system components affect pressure and velocity.
• Safe lab practice: Full compliance with safety protocols.

Learning Objectives Covered

1. Apply the Energy and Continuity equations to practical flow scenarios.
2. Identify and calculate major and minor losses in a fluid system.
3. Use empirical data to calculate loss coefficients for system components.
4. Demonstrate competence in using Pitot tube flow meters for pressure and velocity measurements.
5. Analyze and interpret experimental data to evaluate theoretical predictions.
6. Understand and follow laboratory safety protocols effectively.

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