Z

where H = energy (total head) of system, ft • lb/lb or ft (N • m/N or m) V = velocity, ft/s (m/s)

g = acceleration of gravity, 32.17 ft/s2 (9.807 m/s2) p = pressure, lb/ft2 (N/m2)

g = specific weight (force) of liquid, lb/ft3 (N/m3) Z = elevation above (+) or below (-) datum plane, ft (m)

The velocity and pressure at the point of energy measurement are expressed in units of equivalent head and are added to the distance Z that this point is above or below the selected datum plane. If pressure is measured as gage (relative to atmosphere), total head H is gage; if pressure is measured as absolute, total head H is absolute. Equation 1 can also be applied to liquid at rest in a vertical column or in a large vessel (or to liquids of various densities) to account for changes in pressure with changes in elevation or vice versa.

The equivalent of velocity and pressure energy heads in feet (meters) can be thought of as the height to which a vessel of liquid of constant density has to be filled, above the point of measurement, to create this same velocity or pressure. This is illustrated in Figure 4 and further explained in the following text.

Velocity Head The kinetic energy in a mass of flowing liquid is 2 mV2 or 2 (W/g)V2. The kinetic energy per unit weight (force) of this liquid is 2 (WV2/Wg), or V2/2g, measured in feet (meters). This quantity is theoretically equal to the equivalent static head of liquid that is required in a vessel above an opening if the discharge is to have a velocity equal to V. This is also the theoretical height the jet of liquid would rise if it were discharging vertically upward from an orifice.

A free-falling particle in a vacuum acquires the velocity V starting from rest after falling a distance H. Also

All liquid particles moving with the same velocity have the same velocity head, regardless of specific weight. The velocity of liquid in pipes and open channels invariably varies across any one section of the conduit. However, when calculating system resistance it is sufficiently accurate to use the average velocity, computed by dividing the flow rate by the cross-sectional area of the conduit, when substituting in the term V2/2g.

Pressure Head The pressure head, or flow work, in a liquid is p/g, with units in feet (meters). A liquid, having pressure, is capable of doing work, for example, on a piston having an area A and stroke L. The quantity of liquid required to complete one stroke is gAL. The work (force X stroke) per unit weight (force) is pAL/gAL, or p/g. The work a pump pressure heads spgr = 1.0

pressure equivalent head static pressure intensity

pressure intensity pressure equivalent head static velocity head »2/2g pressure intensity

pressure intensity

FIGURE 4 Equivalent static head

FIGURE 4 Equivalent static head

FIGURE 5 Liquids of different specific weights (also specific gravities) require different column heights or pressure heads to produce the same pressure intensity (43.3 lb/in2 = 298.5 kPa).

must do to produce pressure intensity in liquids having different specific weights varies inversely with the specific weight or specific gravity of the liquid. Figure 5 illustrates this point for liquids having specific gravities of 1.0 and 0.5. The less dense liquid must be raised to a higher column height to produce the same pressure as the denser liquid. The pressure at the bottom of each liquid column H is the weight of the liquid above the point of pressure measurement divided by the cross-sectional area A at the same point, AHg/A, which is simply Hg. Note that in this discussion A is in square feet (square meters) and L and H are in feet (meters).

The height of the liquid column in feet (meters) above the point of pressure measurement, if the column is of constant density, is equivalent pressure static head. When pressure intensity AHg/A is substituted forp inp/g, it can be seen that the pressure head H is the liquid column height. Therefore, at the base of equal columns containing different liquids (with equal surface pressures), the pressure heads in feet (meters) are the same but the intensities in pounds per square foot (newtons per square meter) are different. For this reason, it is necessary to identify the liquids when comparing pressure heads.

Elevation Head The elevation energy, or potential energy, in a liquid is the distance Z in feet (meters) measured vertically above or below an arbitrarily selected horizontal datum plane. Liquid above a reference datum plane has positive potential energy because it can fall a distance Z and acquire kinetic energy or vertical head equal to Z. Also, it requires WZ ft • lb (N • m) of work to raise W lb (N) of liquid above the datum plane. The work per unit weight (force) of liquid is therefore WZ/W, or Z ft (m). In a pumping system, the energy required to raise a liquid above a reference datum plane can be thought of as being provided by a pump located at the datum elevation and producing a pressure that will support the total weight of the liquid in a pipe between the pump discharge and the point in the pipe to which the liquid is to be raised. This pressure is AZg/A, or simply Zg lb/ft2 (N/m2) or Zy/144 lb/in2. Because head is equal to pressure divided by specific weight, elevation head is Zg/g, or Z ft.

Liquid below the reference datum plane has negative elevation head.

Total Head Figure 6 illustrates a liquid under pressure in a pipe. To determine the total head at the pressure gage connection and relative to the datum plane, Eq. 1 may be used (assume that the gage is at the pipe centerline):

FIGURE 6 The total head, or energy, in foot-pounds per pound (newtonmeters per newton) is equal to the sum of the velocity, pressure, and elevation heads relative to a datum place. A unit weight (force) of the same liquid or any liquid raised to rest at the height shown, or under a column of liquid of this same height, has the same head as the unit weight (force) of liquid shown flowing in the pipe.

FIGURE 6 The total head, or energy, in foot-pounds per pound (newtonmeters per newton) is equal to the sum of the velocity, pressure, and elevation heads relative to a datum place. A unit weight (force) of the same liquid or any liquid raised to rest at the height shown, or under a column of liquid of this same height, has the same head as the unit weight (force) of liquid shown flowing in the pipe.

In USCS units

In SI units

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