Question

13.8D Fuel or chemical leaks and spills can have catastrophic ramifications; thus the hazards associated with such events must be well understood. Prepare a memorandum for one of the following: (a) Experience with interstate pipelines shows that propane leaks are usually much more hazardous than leaks of natural gas or liquids such as gasoline. Why is this so? (b) The most important parameter in determining the accidental rate of release from a fuel or chemical storage vessel is generally the size of the opening. Roughly how much faster would such a substance be released from a \(1-\mathrm{cm}\) hole than. from a 1 -mm hole? What are the implications of this?

Short answer

A substance is released 100 times faster from a 1 cm hole than from a 1 mm hole. Larger openings lead to significantly faster release rates, increasing potential hazard.

Step-by-step solution

Understand the Problem

Identify the key aspects of part (b): Calculate the rate of release of a substance from two different hole sizes, compare them, and discuss the implications.

Define Parameters and Formulas

The flow rate from a hole is proportional to the cross-sectional area of the hole: \[ Q \propto A \] where \( Q \) is the flow rate and \( A \) is the area of the hole. The area of a circular hole is calculated using: \[ A = \pi r^2 \]

Calculate the Areas

Calculate the area for both holes. For the \(1 \text{cm}\) hole: \[ r = 0.5 \text{cm}\] \[ A_1 = \pi (0.5 \text{cm})^2 = 0.25 \pi \text{cm}^2 \] For the \(1 \text{mm}\) hole (0.1 cm): \[ r = 0.05 \text{cm}\] \[ A_2 = \pi (0.05 \text{cm})^2 = 0.0025 \pi \text{cm}^2 \]

Compare the Flow Rates

The flow rate ratio is the same as the area ratio: \[ \frac{Q_1}{Q_2} = \frac{A_1}{A_2} = \frac{0.25 \pi}{0.0025 \pi} = \frac{0.25}{0.0025} = 100 \]

Discuss the Implications

A substance is released 100 times faster from a \(1 \text{cm}\) hole than from a 1 mm hole. This implies that larger openings lead to significantly faster release rates, increasing potential hazard and necessitating rapid response and robust containment measures.

Key concepts

Fluid Dynamics: Understanding Flow

Fluid dynamics helps us understand how fluids (liquids and gases) behave. It's a branch of physics concerned with the movement of fluid substances. This field is important in many areas, from designing pipelines to predicting weather patterns. One key principle in fluid dynamics is the equation of continuity, which states that the mass of the fluid that enters a system must equal the mass that exits, assuming the system is closed. Another important concept is Bernoulli's principle, which shows how the speed of a fluid affects its pressure. Understanding these principles allows engineers to predict how fluids will flow through different systems, which is crucial in many industries.

Flow Rate Calculation: Key to Safety

Flow rate calculation is vital in determining how quickly a fluid will move through a given area. It helps in designing efficient systems and ensuring safety. The flow rate can be calculated using the formula: \[Q = A \times v\]here, \(Q\) represents the flow rate, \(A\) is the cross-sectional area of the flow, and \(v\) is the fluid velocity. In the original problem, we calculated areas for different hole sizes using the formula \(A = \pi r^2\). Comparing these areas helped us understand that a larger opening results in a significantly higher flow rate. Calculating flow rates accurately ensures that we can predict and mitigate potential hazards effectively.

Hazard Assessment: Identifying Risks

Hazard assessment is the process of identifying and evaluating potential risks associated with industrial processes. Understanding the rate of fluid release is crucial here. If there's a leak, knowing the flow rate helps predict how quickly a substance will escape and spread. For instance, a larger hole releases substances faster, increasing danger significantly. This assessment is vital for planning emergency responses and designing containment measures. In the case of hazardous substances, quick and accurate hazard assessment ensures safety measures are in place, minimizing risks to people and the environment.