1.2 Concept of Pressure

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1.2 provides a review of pressure. Pressures of liquids and gasses are of significant importance in HVAC applications. Understanding pressure is fundamental to the study of psychometrics because pressure has a direct effect on the properties of moist air. In order to understand pressure, it is necessary to understand the concept of force. This is because pressure by definition is force per unit of area. Written as an equation, Pressure = Force / Area.

Sounds simple, right?Well, actually it is pretty simple.

Pressure is a very simple concept. If the force is measured in units of pounds, and the area is measured in units of feet, then the units for pressure would be pounds per square foot, and this would be written as psf.

An example in calculating pressure is shown here in example 1.2.1. Assume that we have an open tank and this tank is filled with 3,000 lbs of water. The tank dimensions are 2 feet by 3 feet. What is the pressure exerted on the bottom of the tank?

So the solution here is to use the equation for pressure as pressure is equal to the force divided by area. In this example, the force is the weight of the water which is 3,000 lbs. The area is the area on the bottom of the tank, which is 2 feet by 3 feet which equals six square feet. Therefore, the pressure is 3,000 lbs per 6 square feet, which is the same as 500 lbs per square foot written also as 500 psf. Put another way, the water in the tank exerts 500 lbs per every square foot on the bottom of the tank due to the weight of the water. Pressure is a very simple concept but it tends to get confusing due to the variety of applications and units that are used to measure pressure.

As in the example, pressure is measure in pounds per square foot. It can also be measure in pounds per square inch, and often we talk about barometric pressure typically given in something called inches of mercury. HVAC systems very often measure pressure in inches per water column, and plumbers like to use a measurement of pressure in feet or feet of of head pressure.

Understanding pressure is of great importance in HVAC applications, and different applications measure pressure in different ways and in different units. This slide is to help understand the relationship of measuring pressure. The atmosphere exerts pressure on the earth due to its weight. At sea level, the height of the atmosphere is greater than at higher elevations, for example, Denver. So, the atmospheric pressure is greater in San Francisco than it is in Denver.

Pressure gages often measure the difference between the fluid pressure and the atmospheric pressure. So there is a relationship between the pressure measured by the gage and the atmosphere. To understand this relationship, let’s first start with something called zero pressure. The pressure due to the weight of the atmosphere is called atmospheric pressure, which of course is some value above zero pressure, shown as the blue line here in this slide.

Pressure measuring devices typically measure the difference between the pressure of the fluid and the atmospheric pressure shown on this slide as the red line. We’ll call that gage pressure. Typically, gages are calibrated to read zero at atmospheric pressure so that the reading you get for the gage pressure is the difference between the measured pressure and atmospheric pressure. Absolute pressure, gage pressure, and atmospheric pressure are related by the equation: P absolute = P atmosphere + P gage.

As noted earlier, the pressure exerted by a fluid will depend on the weight of the liquid or the gas. The weight, which is the force exerted, depends on the height of that liquid and the density of the liquid or gas. This makes sense, because if you think about it a liquid that is more dense will exert a greater force than a less dense fluid for the same height of the column of fluid.

This relationship is written as an equation P = Density X Height. So there are two columns of liquid of equal height, if they have different densities, they will exert different pressures. If the density is in units of pounds per cubic foot and the height is measured in feet, then the units for pressure are shown in the equation pounds per cubic foot times feet equals pounds per square foot, which equals psf.

Let’s consider another example, example 1.2.2. In this example, a 50ft high pipe is filled with water and extends from the condenser on the top floor of a building to cooling tower on the roof. What is the pressure exerted on the condenser due to the water in the pipe?

Give the answer in units of psi (pounds per square inch). To solve this, we use the equation for pressure where pressure is equal to the density of the fluid times the height of the fluid. In this case, the density is the density of water is assumed to be 62.4 lbs per cubic foot. The height is given in the exampl as 50 ft. The pressure, then, is 62.4 pounds per square foot times 50 ft which equals 3120 pounds per square foot. But the question was not in psf, but in psi, pounds per square inch. To do so, we simply apply unit analysis to convert square feet to square inches using the factor: one square foot = 144 inches squared. Doing the math, we see that the answer comes out to 21.7 pounds per square inch. Please note, this is gage pressure. Why? Because if we put a gage at the bottom of the column, the pressure would read 21.7 psi. If we were to move that same gage up to the top, we would notice that the reading would go down until the very top, where it would read zero. This is because the gage is calibrated to read zero at atmospheric pressure, so the gage is reading the results of the pressure due to the water only.

Let’s look at one more example. Example 1.2.3. In plumbing applications, the terms head pressure, or feet of head is often used as a metric to measure pressure. We often see a conversion factor that plumbers have to use where 2.31 feet of head is equal to 1 psi. The question here is derive this conversion factor. To solve this, we will use the equation pressure is equal to density times height of the column of fluid, where P, pressure, equals 1 psi and D equals the density of water.

First, we need to convert one pounds per square inch to pounds per square foot. Also, we’ll rewrite the equation P = density times height as P divided by density to equal height. Now substitute 144 lbs per square foot, which is the same as 1 psi and insert 62.4 pounds per cubic foot for density. This gives us the following: 144 lbs per square foot divided by 62.4 pounds per cubic foot. Using math and a careful check of the units, we see that this equals 2.31 feet.

This concludes a basic review of pressure. The next tutorial provides a review of enthalpy and sensible and latent heat.