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Fluid (gas or liquid) molecules tend to seek equilibrium (a stability of forces). When forces acting on a fluid are unequal, molecules in the fluid move in the direction of the resultant forces. Therefore, an elementary property of any fluid at rest (not flowing) is that the force exerted on any molecule within the fluid is the same in all directions.
A hydrostatic force is a force exerted by the weight of the fluid against the walls of a vessel containing the fluid.
Hydrostatic pressure, the hydrostatic force per unit area, is perpendicular to the interior walls at every point. If the pressure were not perpendicular, an unbalanced force component would exist and the fluid would flow.
If gravity is the only force acting on a fluid (e.g., the water in a gravity plumbing system), the hydrostatic pressure at any point in the system is directly proportional to the weight of a vertical column of that water. Additionally, the pressure is directly proportional to the depth below the surface and is independent of the size or shape of the container. For example: the hydrostatic pressure at the bottom of a 6 ft (2 m) high pipe that's filled with water is the same as the hydrostatic pressure at the bottom of a tank or pool that's 6 ft (2 m) deep. A 12 ft (4 m) pipe that's filled with water, and slanted so that the top is only 6 ft (2 m) above the bottom (measured vertically), will have the same hydrostatic pressure exerted at the bottom of the 6 ft (2 m) vertical pipe even though the distance along the 12 ft (4 m) pipe is much longer.
Water pressure difference is the driving force behind fluid flow.
Water pressure available at the water service is lost as water flows through the piping of a plumbing system. This pressure loss or pressure drop in a plumbing system is from friction loss as the water moves through the system and pressure loss as water is forced to a higher elevation (e.g., from the basement to an upper story).
Water pressure available at the water service is considered acceptable in the range of 40 to 80 psi (275 to 550 kPa) or greater in mountainous regions. In most residential and commercial systems, the upper limit is 80 psi (550 kPa). Some systems with thermoplastic supply piping set the upper pressure limit much lower, usually about 40 psi (275 kPa). When water service pressure is deemed too great, a pressure reducer is used to limit pressure and reduce potential for leaks in the thermo plastic supply piping.
An insufficient pressure at a plumbing fixture results in low flow of water at that fixture. An excessive pressure at a fixture may cause disturbingly high flow, will waste water, and may cause damage to or premature deterioration of the fixture.
Residual water pressure is the pressure available at the outlet, just before a fixture. It affects water output of a fixture.
The residual pressure requirement at the many types of plumbing fixtures varies. Code specifies that the highest (most remote outlet) fixture have a minimum pressure of 8 psi (55 kPa) for flush tanks and 15 psi (103 kPa) for fixtures with flushometer valves. Tbl. 1 provides recommended residual pressure for different plumbing fixture types.
When forces acting on a fluid are unequal, molecules in the fluid move in the direction of the least pressure. Fluid flow is caused by a pressure difference in the fluid. A fluid will always flow from a higher pressure region to a lower pres sure region. A pressure difference must exist at a plumbing fixture to cause water to flow-that is, water pressure at the fixture must be at a higher level than atmospheric pressure for water to flow from the fixture. Pressure difference (delta_P) is the driving force of fluid flow.
Pressure Difference from Elevation Change (Static Head)
In the building plumbing supply system, water is the fluid under consideration. Water has a maximum specific weight of 62.4 lb/ft 3 . So at its maximum weight, a 1 ft by 1 ft by 1 ft cube of water exerts a maximum force of 62.4 lb at its base, which equates to a pressure of 62.4 lb/ft 2 or a pressure of 0.433 psi at the base of the cube (62.4 lb/ft^2 divided by 144 in2 /ft^2 _0.433 lb/ in^2). Therefore, a 1 ft high column of water creates a pressure of 0.433 psi at its base; a 2 ft high column exerts a pressure of 0.866 psi at its base (2 · 0.433 psi); a 3 ft column, 12.99 psi at its base (3 · 0.433 psi); and so on.
In a plumbing supply system, pressure difference from elevation change or simply static head (delta_P_static) is found by multiplying the vertical height (Z), in feet, by the factor of 0.433 psi/ft. By convention, the vertical height (Z) is positive if elevation increases from the station with the known pressure (the station is higher than the station with the known pressure) and negative if elevation decreases.
static head, in psi, delta_P_static __0.433Z In the SI (metric) units, where vertical height (Z) is measured in meters:
static head, in kPa, delta_P_static __9.8Z Pressure difference is negative (a loss) if the elevation change from the known pressure is upward (a positive Z) and positive if elevation change is downward (a negative Z).
Pressure change in a plumbing system from elevation change may be computed by multiplying the vertical height of the fixture outlet to the street main (a known pressure) by the pressure the water creates per foot. Conversely, a 2.31 ft of elevation change results in a pressure difference of 1 psi and a 0.102 m change results in a pressure difference of 1 kPa.
ILL. 6 Pressure loss from friction caused by water flow in smooth pipe (copper tubing), based on flow rate and pipe diameter.
A plumbing fixture outlet is 24 ft above the water service line.
Pressure available at the water service is 45 psi.
a. Determine the change in pressure from elevation. Change in elevation is upward from the known pressure, so delta_P_ is negative.
b. For pressure available at fixture: 45 psi _ (_10.4 psi) _ 34.6 psi available at fixture outlet __10.4 psi (a 10.4 psi loss)
delta_P_static __0.433Z __0.433(24)
Pressure Losses from Friction
Pressure losses from friction, friction head (delta_P_friction), are more difficult to compute, as they are related to flow rate (gpm, L/min or L/s), fluid velocity (ft/s or m/s), pipe diameter, pipe material and surface roughness, pipe length, and number of fit tings and valves. Experimentation has led to a variety of pres sure drop charts for pipes of many different materials. Pressure drop charts are provided in Ills. 6 through 8. A review of the pressure drop chart in Ill. 6 for water in smooth pipe shows that pressure drop is related to water flow rate, velocity, and nominal pipe diameter.
The pressure drop chart in Ill. 6 applies to smooth pipe, such as copper and plastic pipe and tubing. Pipe diameters from 3/8 to 1 in are also based Types K, L, and M copper tubing sizes; refer to the legend in the upper left hand corner of the chart. Beyond 1 in diameter tubing, pressure drop disparity with difference in wall thickness is negligible.
Ill. 7 applies to friction loss in rough pipe, such as steel and iron pipe. Roughness of the inner walls of pipe influences friction loss. Pressure drop for a particular rough pipe diameter is greater than in a smooth pipe having the same inside diameter.
The pressure drop chart in Ill. 8 applies to pressure drop as water flows through a water meter. Water meter design typically reduces pressure significantly. It should not be neglected in pressure drop computations.
Pressure drop charts have many lines and numbers; use them with care and review the information on the chart before using it. Along the left and right is the volumetric flow rate, and along the bottom and top is the friction loss in the pipe. On the charts provided, pressure drop from friction is expressed in psi per 100 ft. The heavy, solid lines sloping diagonally to the left represent the nominal diameters of pipe; the lines running perpendicular (at a 90° angle) to the pipe diameter lines represent the velocity of the water in a pipe of a specific nominal diameter.
ILL. 8 Pressure loss in a water meter, based on flow rate and meter size.
a. Determine the pressure drop across a 1 in diameter Type L copper pipe that's 20 ft long and is carrying water at 20 gpm.
From Ill. 6, at 20 gpm a 1 in diameter Type L copper pipe (center line) has a pressure drop of about 10 psi per 100 ft. Thus: delta_P_friction _ (10 psi/100 ft) _ 20 ft _ 2 psi loss or _2 psi
b. Determine the velocity of water flowing in a 1 in diameter Type L copper pipe carrying water at 20 gpm.
From Ill. 6, at 20 gpm and for 1 in diameter Type L copper pipe, the velocity is about 7.8 ft/s.
c. Determine the pressure drop across a 4 in diameter Type K copper pipe that's 236.5 ft long and is carrying water at 400 gpm.
From Ill. 6, at 400 gpm a 4 in pipe has a pressure drop of about 3.5 psi per 100 ft. Thus: _ 8.3 psi loss or _8.3 psi
delta_P_friction _ (3.5 psi/100 ft) _ 236.5 ft
d. Determine the velocity of water flowing in a 4 in diameter Type K copper pipe carrying water at 20 gpm. From Ill. 6, at 400 gpm and for 4 in diameter Type L copper pipe, the velocity is about 10 ft/s.
In addition to pipe length, friction loss from fittings and valves must be taken into account. Analysis is usually founded on the equivalent length based on type of valve or fitting.
Tables 2 and 3 indicate the equivalent length, in terms of friction losses, for various types and sizes of valves and fittings for tubing (smooth pipe) and threaded pipe. Tables 2a and 3a are in customary units and Tables 2b and Tables 3b are in modified metric (SI) units.
As a minimum, pressure drop analysis should be per formed to ensure that pressure available at the most remote out let (farthest and highest fixture) is adequate. This proceeds once the layout of the plumbing system has been performed. Thus, the constant velocity method may be used in initial sizing.
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