In fluid mechanics, pressure and head are core parameters for evaluating pump performance, especially for rotary pumps widely used in industrial applications. Rotary pumps transport fluid through the rotational motion of rotors, and their design relies on a precise understanding of pressure and head. Simply put, pressure represents the force per unit area exerted by the fluid, while head indicates the height to which the fluid can be lifted.

· For a unit volume of liquid, its gravitational potential energy is mgh, where m is the mass of the liquid, g is the gravitational acceleration (approximately 9.8 m/s²), and h is the height at which the liquid is located, which is the head.

· The pressure energy of the liquid is PV, where P is the pressure and V is the volume of the liquid.

When liquid flows from one pressure region to another, the change in pressure energy equals the change in gravitational potential energy. Assuming the liquid is at height h₁ under pressure P₁ and at height h₂ under pressure P₂, the equation is:

P₁V - P₂V = mgh₂ - mgh₁

Since m = ρV, where ρ is the density of the liquid, substituting into the above equation gives:

P₁ - P₂ = ρgh₂ - ρgh₁

Assuming P₁ is the reference pressure (usually taken as atmospheric pressure and can be neglected), P₂ is the pressure in question, and h₂ - h₁ is the head H, the equation can be simplified to: P = ρgH

Calculation of Head Corresponding to 1 kg of Pressure

A pressure of 1 kilogram-force per square centimeter (kgf/cm²) is converted to the International System of Units. 1 kilogram-force is equal to 9.8 Newtons, and 1 square centimeter is equal to 0.0001 square meters, so 1 kgf/cm² = 9.8 N / 0.0001 m² = 98,000 Pa.

For water, the density ρ is approximately 1000 kg/m³, and the gravitational acceleration g is 9.8 m/s². Substituting the pressure P = 98,000 Pa, ρ = 1000 kg/m³, and g = 9.8 m/s² into the formula P = ρgH gives:

98,000 = 1000 × 9.8 × H

Solving the equation yields: H=10 meters

This means that, at normal temperatures, for water, 1 kg of pressure is approximately equal to 10 meters of head.

Impact of Different Liquids

Different liquids have different densities, so the head corresponding to the same pressure also varies. According to the formula H = P / ρg, the greater the density of the liquid, the lower the head achievable under the same pressure; conversely, the smaller the density of the liquid, the higher the head under the same pressure. For example, the density of mercury is approximately 13,600 kg/m³. Substituting this into the formula shows that 1 kg of pressure corresponds to a mercury head of approximately 0.735 meters.

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