Pressure

Pressure is the force per unit area that would be exerted on an imaginary small plane area at the point of interest. Your eardrum feels the pressure of the water (until you equalize) regardless of whether your ear is pointing down, up or sideways in the water. The pressure on you ear is the same each way as long as it is at the same depth in the water. Pressure is everywhere the same at the same depth (as long as the fluid is static).

If the fluid is moving there can be changes of pressure along a given horizon. Consider drifting towards an underwater water intake for a factory. The water pressure on your far side is greater than on the near side to the inlet. You feel this as the water drags you along towards the inlet. (Be careful!!)

Pressure – Measurement

Pressure is measured in two ways: Absolute and Gauge Pressure.

Absolute Pressure

Absolute pressure is the formal expression of the total force per unit area. It includes the pressure from the atmosphere (air pressure), the pressure from any external forces applied to the fluid and the pressure resultant from the weight of the fluid itself.

Gauge Pressure

Gauge pressure is the difference in pressure from the atmospheric pressure that typically works in all directions and at all locations open to air. As such the air pressure tends to cancel out in our analysis. Therefore if we consider only the pressures relative to atmospheric (positive or negative) then our computations are often simpler. Atmospheric pressure is typically in the range of 15 psi. An absolute pressure of 25 psi would be equivalent to a gauge pressure of 10 psi. An absolute pressure of 15 psi would be equivalent to a gauge pressure of -10 psi. Typically we use psi (lbs/ ft2 ) for both absolute and gauge pressures.

Pressure “Head”

Other measures of pressure that we need to pay attention to in the on-site industry include pressure expressed as feet of water, inches of water or inches of mercury. These columns of liquid are used as measures of pressure because of their convenience. The amount of rise or fall of liquids in tubes connected to components that have pressures we want to measure is often used as the measure itself:

a. 1 ft of water exerts a downward force of 62.4 lbs/ft3 / 144 in2 = 0.433 psi.

b. 1 inch of water would exert a downward force 1/12 of what 1 ft would cause. Therefore 1 inch of water is equivalent to 0.036 psi

c. Since mercury has a specific gravity of 13.6 we see that 1 inch of mercury would be equivalent to 13.6 inches of water or 13.6 x 0.036 psi or 0.486 psi.

As anyone who has ever gone swimming underwater knows, water pressure increase with the depth of the dive.

Pabsolute = Po + depth * 0.433 psi /ft where Po is the atmospheric pressure.

Po = Atmospheric pressure = 14.7 (+/-) at sea level

Atmospheric pressure = 11.5 (+/-) at 7000 ft (+/-)

If we are interested in gauge pressure it becomes:

Pgauge = depth * 0.433 psi/ft

Or if you want to use ft (head) as your measure,

P = 1 ft /ft.

For example, 10 feet down in the water

Pabsolute = 15 psi + 0.433 psi/ft x 10 ft = 19.33 psi

Pgauge = 0.433 psi/ft x 10 ft = 4.33 psi

Phead = 10 ft

Almost all of the water pressure devices we use measure gauge. It is easy to know, however, because if it is measuring absolute pressure it will read about 15 psi just in the air.

Manometer

The manometer is a useful device for measuring gauge pressure in the field because all it takes is a clear tube and a ruler.

Buoyancy

Buoyancy is considered here because it is a direct consequence of pressure considerations. As we learned water pressure is proportional to depth, and works all around the perimeter of an object either containing the water or suspended within the water. You float in water because you have a specific gravity of about 0.98. If you weigh 135 lbs gravity is pulling you down with a force of 135 lbs. In water, however, there is pressure all over your body that increases with depth. The horizontal components of this force tend to cancel out leaving only the net upward force of the pressure. Consider a simple box anchored by a chain to the bottom of a tank. The overall force tending to float the box (which is being resisted by the chain) is the net result of the difference between the weight of the box and its contents and the pressure that surrounds the box. The pressure on the sides of the box acts in equal and opposite directions and, therefore, cancels. The pressure differential from bottom to top results in the net upward force of buoyancy.

Consider a septic tank set in an area, which is subject to seasonal high ground water. The water surrounds the tank and even though the tank is not in a large lake the surrounding water exerts the same pressure it would if the tank were submerged to the same depth in a large tank.

To determine if the tank will tend to float up breaking its inflow and outflow pipes (and possibly contaminating the area with partially treated wastewater, thereby creating a public health problem as well as an environmental problem) it is necessary to do a buoyancy analysis. To do such an analysis the following data is necessary:

a. a. The weight of the tank empty. (Wt) This force acts downward. This can be computed by calculating from the inside dimensions and outside dimensions the total volume of concrete. (Don’t forget the baffles.) With the volume of the concrete and its specific gravity the total weight of the tank can be computed. Or, simply call the tank manufacture who will certainly be able to tell you the total tank weight.

b. b. The weight of the maximum displaced volume of water that would otherwise fill the place where the tank is (B). This, as discussed above, is the buoyant force that acts upward on the tank. Length (ft) x Width (ft) x Height (ft) x 62.4 lbs/ft3 = Total Buoyant Force (B)

c. c. The weight of the minimum amount of water that will be in the tank. (Ww) The conservative approach might be to consider this amount of water to be zero gallons, pounds, cubic feet, or depth. Example, if a homeowner has his septic tank pumped during the spring (when his system is not working because of groundwater) and the pumper drains the entire tank. With pressure dosed systems there is usually a minimum amount of water below the lowest (off) float.

d. d. The weight of any soil directly over the tank. (Ws) This can be computed by knowing the length and width of the tank, the specific gravity of the soil, and the anticipated minimum cover depth.

Putting it all together, if:

Wt + Ww + Ws > B the tank will not float

If,

Wt + Ww + Ws < B the tank will float.

Generally, the tank will not rise up and partially stick up above ground (but it possibly could). Actually this might not be as bad as what would most likely happen. Instead the tank will slowly, gradually move up pulling at its pipes. As it moves up the water level around it will drop until more water comes into the void around the tank. Then it will rise again and the process will repeat until the pipes break. Furthermore, we have ignored the shear forces between the overburden soil and the surrounding native soul and between the tank and the backfilled material. These shear forces can slow down the process and may even stop it but eventually as the soils become saturated these forces tend to get smaller.

Continuity

The concept of continuity is a simple one. You use it every time you balance your checkbook:

Deposits – Withdrawals = Change in Balance

In hydraulics:

Total Inflow – Total Outflow = Change In Volume

Or seen another equivalent way,

Final Volume = Initial Volume + Total Inflow – Total Outflow

Continuity in Closed Systems

In a closed and filled system where there is no place for either additional storage or release of water continuity simplifies to:

Deposits – Withdrawals = 0

Or,

Deposits = Withdrawals

This simpler approach to continuity is useful in closed and filled pipe systems.

In the above system the flow in (Q) must equal the flow out (Q) because there is nowhere for extra water to be stored or released from which would otherwise allow the flow in to be different from the flow out.

Where there is additional space for added storage and/or releases the inflow need not equal the outflow at all times. Consider a simple septic tank with flows both coming in and going out. If they are not equal there must be change in volume.

Continuity in Open Systems

Using flow rates make things a bit more complicated but not much.

Inflow (rate) x Inflow time – Outflow (rate) x Outflow time = Change in Volume

Or seen another way,

Final Volume = Initial Volume +Inflow (rate) x Inflow time – Outflow (rate) x Outflow time

Continuity for Water in Motion

Continuity for water in motion allows the computation of the average velocity of the water in the conduit. If the average velocity at a point is called V and the area of the conduit is A the total flow at that point is V x A. This must equal the total flow Q, Therefore Q = V x A Since the flow must remain constant if there is no place for storage or release this must result in V x A being the same all along the conduit: V1 x A1 = V2 x A2 = V3 x A3 etc etc = Q