 # Tag Archive: Weight

## Hydrostatic Pressure

In one application I’m working on I need to supply hydraulic pressure to the unit what placed at the height approx 100 ft. I decided to calculate the pressure losses created by the height only for the pump at the land HPU.

The height difference creates hydrostatic pressure (what is a pressure drop for the pump) what can be calculated from Pascal’s law: $\triangle p=\rho\cdot g\cdot(h_2-h_1)=\gamma\cdot(h_2-h_1)$

here: $\begin{array}{l}\rho\;-\;oil\;density\;(slugs/ft^3)\\g\;-\;acceleration\;due\;to\;gravity\;(32.174\;ft/s^2)\\\gamma\;-\;specific\;weight\;of\;the\;oil\;(lb_s/ft^3)\end{array}$

The specific weight (the weight per unit volume of a material) of the mineral oil on Earth is approx.: $53.57\;lb_s/ft^3 = 0.031\;lb_s/in^3$ (at environment temperature 40°C for oil with ISO Grade 46)

So, for 1 ft (for 12 in) of height we get pressure drop in PSI: $\triangle p=0.031\;\frac{lb_s}{in^3}\cdot12\;in\;=\;0.372\;psi$

Therefore, for 100 ft the pressure drop is 37.2 psi = 2.57 bar only.

The calculations look very easy, but one problem I found in internet: many sources mix density and specific weight. For example, at The Engineering Toolbox you can find value of density of the water $62.4 \;lb_s/in^3$. But it is not right, because this value is a specific weigh of the water, not a density! The density of the water is: $\rho_{water}=\frac{\gamma_{water}}g=\frac{62.4\;lb/ft^3}{32.174\;ft/s^2}\;\;=\;1.94\;slugs/ft^3$

It has to be clear: the density is mass per unit volume, this is constant at any places (on Earth, on Moon, on any height., etc.) and it is different from specific weight.

## Mass and Weight

Summary:

• Difference between Mass and Weight
• Difference between lb, lbf, lbs, lbm

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To calculate cylinder forces we have to operate with mass and weight.

Mass is a fundamental property of the object, a measure of the amount of matter in the object. The “kilogram” (kg) is the SI unit of mass and it the almost universally used standard mass unit. The “pound” (lbm or simply lb) is the unit of mass in the imperial system.  In all scientific work is strongly recommended instead “pound” (lb) use “pound mass” (lbm).

Usually, people write lb when they are talking of one pound or a single pound and write lbs to indicate the fact that they are talking about many pounds. Thus, they use lbs as a plural for lb that stands for a pound. But lb is the correct abbreviation to be used both as singular as well as plural.

If an object has a mass of 1 kg on the Earth, it would have a mass of 1 kg on the Moon, even though it would weigh only one-sixth as much.

1 lbm = 0.45359237 kg

There is also a unit of mass called the slug, defined as the mass which exerts a force of 32.174 049 lbs under the gravitational acceleration at the earth’s surface:

1 slug = 32.174049 lbm

But even in US the use of exclusively SI units for all scientific work is strongly encouraged.

Weight is the force on the object, caused by the gravity and may be calculated as the mass times the acceleration of gravity:

W = F = mg

Acceleration of gravity at the Earth’s surface: g=9.81 m/s2 (approx. 32.174 ft/s2)

The Newton (N) is the SI unit of weight. In the US the pound force unit, abbreviated lbf, is a unit of weight:

1 lbf = 1 slug × 1 ft/s2 = 32.17405 lbm × 1 ft/s2 = 32.17405 lbm × ft / s2

1 lbf = 0.453 592 37 kg × 9.80665 m/s2 = 4.44822162 N