Sizing alloy steel pipes for industrial applications is a critical engineering task that directly impacts system efficiency, safety, and longevity. Unlike simpler, less demanding systems, industrial settings often involve extreme temperatures, high pressures, and corrosive media, all of which demand meticulous pipe selection. This isn't a game of guesswork; it's a process that requires a solid understanding of fluid mechanics, material properties, and application-specific requirements.

Let's break down the key factors that influence alloy steel pipe sizing:

1. Flow Rate and Velocity:
First, you must determine the required flow rate of the fluid (liquid or gas) through the pipe. This dictates the volume of material moving within a given time. Flow rate is typically measured in gallons per minute (GPM), cubic meters per hour (m³/hr), or similar units. Once you know the flow rate, you’ll need to consider fluid velocity. In piping, you’re walking a tightrope. Too low, and you risk sedimentation and inefficient heat transfer. Too high, and you could end up with erosion, increased pressure drops, and noise. 

For liquids, a general recommendation is to maintain velocities between 5 and 10 feet per second (fps). For gases, the velocity can be higher, sometimes reaching 40-60 fps, depending on the application and pressure. However, remember, these are guidelines, not hard-and-fast rules. Specific industrial processes may demand tighter velocity ranges. It's always a good idea to consult with fluid mechanics experts for nuanced situations, particularly with multiphase flows.

2. Pressure Drop:
Every fluid moving through a pipe experiences friction, which results in a reduction of pressure along the pipe’s length. This pressure drop (also known as head loss) is a fundamental consideration in pipe sizing. Excessive pressure drop translates to higher energy consumption by pumps or compressors, and it can lead to inadequate delivery at the point of use.

Several factors affect pressure drop: pipe length, diameter, material roughness, fluid viscosity, and flow velocity. It's governed by equations like the Darcy-Weisbach equation or Hazen-Williams for water flow. While calculations are essential, don't shy away from utilizing online calculators and software specifically designed for pipe flow calculations. These tools help to account for a multitude of variables and can save you significant time and effort. The iterative nature of this calculation can be tedious when done manually, so embrace modern aids.

3. Material Considerations:
Alloy steel is chosen for its superior strength, corrosion resistance, and ability to perform under extreme temperatures and pressures. However, “alloy steel” is an umbrella term encompassing a vast array of specific alloys, each with its unique properties. When selecting the right alloy, look at the following:

• Corrosion Resistance: Different alloys offer varied resistance to different chemicals, acids, and alkalis. Make sure the chosen alloy can withstand the specific environment you are operating in. Consider the potential for pitting, crevice corrosion, and uniform corrosion. If you're handling highly corrosive media, you need to be extremely careful and possibly consider additional protective measures like coatings.
• Temperature Range: High-temperature processes such as steam lines require alloys designed for high-temperature creep resistance, while low-temperature applications demand impact strength at lower temperatures. Check the manufacturer’s material data sheets for temperature limits and performance changes under different temperature ranges.
• Mechanical Strength: Understand the tensile strength, yield strength, and fatigue limit of the alloy. These values dictate the pipe's ability to withstand internal pressure and external loads without deformation or failure. 

4. Wall Thickness and Schedule:
The pipe wall thickness and schedule (a numerical value indicating relative thickness) are a function of the pipe diameter and the operating pressure. Higher pressure requires a thicker pipe wall. Pipe schedules are standardized in specifications like ASME B36.10 and ASME B36.19 for stainless steel pipes. You must select a schedule that ensures the pipe can safely withstand the maximum operating pressure with a comfortable safety factor. It’s not enough to just meet the minimum requirements; consider potential pressure surges, water hammer, and future system modifications.

5. Practical Considerations:
Beyond the pure engineering calculations, there are a few real-world aspects to take into account:

• Pipe Availability: Sometimes, the "ideal" pipe size might not be readily available, or it may come with significant lead times. Work with your suppliers early in the project to determine the accessibility of your desired dimensions and schedules.
• Cost: Larger-diameter, thicker-walled pipes naturally cost more, both in material and installation. The cost-benefit of slightly oversized piping should be carefully balanced against long-term operational costs.
• Installation: Consider the practicalities of installation, including handling, joining methods (welding, threading, etc.), and available space for laying out pipes. Remember that the best design on paper is useless if it cannot be implemented efficiently.
• Future Scalability: It's prudent to consider future expansion or changes to your system. Oversizing the pipe slightly, if practical, may save significant costs and headaches later.

A Note of Caution:
Pipe sizing is not a linear process. It's an iterative loop where you might need to adjust several parameters to arrive at the most optimal solution. Don’t hesitate to consult piping engineers who specialize in this area for complex projects. Software tools are valuable, but they are ultimately aids, and they don’t replace a deep understanding of the underlying physical principles. Always double-check your calculations and ensure compliance with relevant standards and regulations. The cost of getting this wrong is rarely worth the shortcut.