You may wonder how pipes and hoses can withstand the large pressure of water running through them. Much of this comes down to understanding the physics behind them. Engineers check these standards by testing how strong hoses are, and the Maximum Allowable Working Pressure (MAWP) is a key tool in setting safe limits for a hose.

## Maximum Allowable Working Pressure (MAWP)

You can calculate the **Maximum Allowable Working Pressure (MAWP)**, the maximum pressure for a hose, using the formula

for MAWP value *P* in psi, yield strength (or tensile strength) of the material *S _{y}*, design factor

*F*, longitudinal joint factor

_{d}*F*, temperature derating factor

_{e}*F* and interior pipe diameter

_{t}*d*. These factors take into account features of the materials themselves, and you'll need to look them up for the materials involved in the specific case you're considering.

_{o}For example, if you knew the inside diameter of a cylindrical vessel were 200 inches, you could figure out how to use a metal alloy to create it. Use a carbon steel material with a yield strength of 64,000 psi that has a thickness of 1/2 inch. The design factor is 0.72, the longitudinal joint factor is 1.00 and the temperature derating factor is 1.00. Using the formula, you can calculate a MAWP as:

## MAWP Standards

As MAWP is defined by the International Organization for Standardization, pressure vessels generally have design parameters for their various characteristics such as wall thickness or the interior radius of hose vessels. Engineers check them closely to make sure their designs can withstand their appropriate pressure, temperature, corrosion and whatever else may hinder their performance. Tests that use pressurized water determine the hydrostatic test pressure to make sure that the vessels can withstand the appropriate forces of its use. Manufacturers may use other tests as well.

For example, the company Penflex reduces their MAWP calculations by 20 percent to account for the heat involved that affects yield strength of their braid wires during the welding process. They even take into account adjustment factors that affect MAWP at high temperatures.

The American Society of Mechanical Engineers has set standards such that vessels must meet 100 pounds per square inch (100 psi) and must have a sufficient volume to contain 10,000 gallons of liquid. The example above of 230.4 psi MAWP meets the required 100 psi pressure rating.

## Alternative Design Pressure Formula

You can also test the durability of a vessel using Barlow's formula, *P =* 2*St* / *D*, for pressure *P*, allowable stress *S* in psi, wall thickness *t*, and external diameter *D* to test how the internal pressure of a pipe holds up against the material's strength. When using this formula, ensure *t* and *D* have the same units so that both sides of the equation remain balanced.

You can use Barlow's formula to calculate internal pressure, ultimate bursting pressure, maximum allowable operating pressure (MAOP) and the Mill hydrostatic pressure. You calculate internal pressure by using yield strength for allowable stress *S* and calculating the resulting pressure. Similarly, you can calculate ultimate burst pressure by using the maximum yield strength for *S*.

Use the Specified Minimal Yield Strength (SMYS) for *S*, or the strength associated with a certain specification, to determine MAOP. The Mill Hydrostatic pressure uses the a fraction of the specified yield strength, the stress at which a specific amount of plastic deformation is produced, for *S*. This specified yield strength is generally 60% of the maximum yield strength.

#### References

- Pressure Vessel Engineering: Maximum Allowable Working Pressure
- Penflex: How We Calculate Maximum Allowable Working Pressure (MAWP)
- Science ABC: What Is Ultimate Tensile Strength?
- The Engineering Toolbox: Barlow's Formula - Internal, Allowable and Bursting Pressure
- Cornell Law School Legal Information Institute: Longitudinal Joint Factor (E) for Steel Pipe

#### Resources

- Cornell Law School Legal Information Institute: 49 CFR § 192.113 - Longitudinal joint factor (E) for steel pipe.