In this essay we will discuss about:- 1. Introduction to the Hydraulic Design of Pressure Pipes 2. Determination of Loss of Head in Pipes 3. Minor Head Losses in Conduits 4. Determining Thickness of Metal Conduit 5. Pressure due to External Load on Pipes 6. Temperature Stresses on Pipes.
Essay # 1. Introduction to the Hydraulic Design of Pressure Pipes:
Water pressure pipes can be laid at any depth below the hydraulic gradient line, the velocity in the pressure pipes directly depends on the pressure head at the point of reference. If the velocity of the water is kept very low, large diameter pipe will be required to carry the required quantity of water from one place to another.
On the other hand if too high velocity is allowed in the pipes, cost of pumping will be too high to develop the required pressure, as well as the cost of pipe and its fittings will increase to bear the extra pressure developed. Therefore, it is most necessary to design the pressure pipes in such a way, as the overall cost of the project should be lowest possible, both from constructional and maintenance point of view.
For economy, usually the pipe line should hug the hydraulic gradient line in profile and the straight line in plan. The hydraulic gradient line should neither too high nor too low. In addition to this requirement velocity should be self-cleaning i.e., no silting should be allowed in the pipe line. While designing the pressure pipes acting as gravity main for conveyance of water, the normal velocity of water is kept between 0.9 m/sec. to 1.5 m/sec. for satisfactory results.
ADVERTISEMENTS:
The common practice is to design the pressure pipes acting as gravity mains such that the available pressure head between the source and the city is just lost in overcoming the friction losses.
Essay # 2. Determination of Loss of Head in Pipes:
The loss of head in the pipes can be determined by the following formulae:
(A) Manning’s formula:
The formula is usually used in determining the loss of head in the gravity conduits. This is equally applicable to the turbulent flow in pressure pipes.
ADVERTISEMENTS:
This formula is:
Where, m = Manning’s rugosity coefficient
L = Length of the pipe line in metres
ADVERTISEMENTS:
R = Hydraulic mean depth of pipe
V = Velocity of flow in m/sec.
If d be the diameter of pipe, the value of R will be.
(B) Hazen-Wiliiam’s formula:
Where, CH = Coefficient of hydraulic capacity as given by Table 8.1
S = Slope of the energy line.
V and R are the as in formula 8.1.
ADVERTISEMENTS:
This formula is widely used now a days in designing the pipe lines.
The value of coefficient ‘CH‘ is more for smoother pipe and less for rough pipe. As with the age the inner surface of most of the materials becomes more and more rough. Therefore, the carrying capacity of the pipe lines decrease with the age.
Modified Hazen’s Williams’s Formula:
Sometimes, the most widely used Hazen’s William’s Formula is not preferred due to its limitations:
(i) The Hazen William’s Coefficient CH is not a dimensionless parameters but has the units of L-0.37 T-1. Hence, its value changes with change in the employed units.
(ii) The numerical constant of 0.85 (in M.K.S. units) has been calculated for an assumed hydraulic mean depth (R) of 0.3 m and friction slope of 1/1000. However, the formula is used for all ranges of pipe dia and friction slopes. This practice may lead to an error up to ± 30% in the evaluation of velocity, and ± 55% in head loss due to pipe friction.
Considering these limitations of Hazen William’s formula, a modified Hazen William’s formula has been derived for use from Davey Weisbach and Cole-brook-white equations, which obviates those limitations the modified Hazen-William’s formula states that
(C) Darcy-Weisbach-Formula:
Where, HL = loss of head in m
L = Length of pipe in m
d = diameter of the pipe in m
V = mean velocity of flow through the pipe in m/sec
g = acceleration due to gravity
f = friction factor, its value generally varies from 0.02 to 0.075.
The approximate value of f can be determined by the following empirical formulae:
Formulae
The above formulae (8.5) and (8.6) indicate that the value of friction factor is double in old pipes than its value in new pipes.
Following solved examples will clearly illustrate the method of designing of the pressure pipes:
Example 1:
Water is to be supplied to a town of population 1.5 lakh. If the water works is situated at a lower elevation of 50 metres than the water level in the source. Determine the size of the gravity main to convey the water from source to the water work, if the length of the gravity main is 25 km, and the per capita demand of the town is 150 litres/day/capita.
Take value of f = 0.075.
Solution:
Example 2:
Water is to be supplied to a town of 2 lakh population from a source 1.5 km away. Per capita demand of the town is 180 litres/day/capita. If the town is situated at a higher level than the source and the difference in elevation between the lowest water in the source to the point of inlet at the water works is 27 m. Determine the size of the rising main and HP. of the pump. The value of the CH = 110 and the pump works for 18 hours.
Solution:
Example 3:
Determine the hydraulic gradient in a 90 cm diameter old cast iron pipe carrying a discharge of 0.75 cu m/sec by using (a) Manning s formula, (b) Darcy Weisbach formula and (c) by Hazen-William formula. Assume suitably any data not given.
Solution:
Essay # 3. Minor Head Losses in Conduits:
When different diameters of pipes are connected in series then the total head loss is equal to the sum of loss of head in individual pipe. In addition to this minor losses at each size change of pipe also occur.
In addition to this, if valves and fittings are provided in the pipe line, these all also cause loss in head. While calculating the actual loss in head if possible the minor losses due to the above should also be accounted for. These losses are represented in terms of V2/2g and Table 8.2 gives their common values.
Essay # 4. Determining Thickness of Metal Conduit:
The thickness of the steel or cast iron pipe can the determined from the following formula directly
Where, t = thickness of the pipe shell
d = dia of the pipe
p = internal water pressure
n = efficiency of the joint [for steel pipes it is generally taken as 0.9 for welded, 0.75 for double riveted and 0.63 for single riveted]
ft = permissible tensile stress in the metal of pipe [generally taken as 770 kg/cm2 for CI pipes and 1260 kg/cm2 for steel pipes]
To make corrosion allowed, the value of t obtains by the above formula is increased by 3 to 4 mm.
Essay # 5. Pressure Due to External Loads on Pipes:
To protect the pipes from the damage and atmospheric actions generally they are laid in the ground at reasonable depths. When the pipes are buried in the ground and laid along the road, they have to bear their own load, weight of the back fillings at the top and the superimposed load of the traffic moving on the ground.
These all loads produce compressive stress in the pipe. When the water is flowing at pressure inside the pipe, the external loads are compensated by the water pressure. If the external pressure is more, pipe will have to bear compressive force. If the internal water pressure is more, they will be subjected to the tensile force.
The stresses developed in the pipes due to external loads can be determined by using the following empirical formulae. These formulae have been developed in U.S.A.
For pipes resting on or projecting above the undisturbed ground is cohesionless-soil and covered with fills. Such as in a highway culvert (Fig. 8.1).
The external load likely to come per unit length of pipe is given by:
Where, CP = a coefficient whose values are given in Table 8.3
Y = specific weight of the back fill material above the pipe
D = external diameter of the pipe
W = external load per unit length of the pipe.
(B) For flexible pipes (such as steel pipes) burried in narrow trenches and thoroughly compacted side fills, such as shown in (Fig. 8.2), the external load per unit length of pipe is given by:
where, C = coefficient characteristic of the fill material and the ratio H/B. Typical values are taken from table 8.4.
(C) Following formula is used for determining the external loads coming on the rigid pipes each such as concrete, C.I. or vitrified clay pipes.
where W, C, g and B have the same meaning as above.
(D) Equations (8.8), (8.9) and (8.10) are used in determining the load on pipes due to back filling-over the pipes in trenches.
Thus value of super imposed load due to moving traffic on the ground, which is transferred to the pipe, is determined by the following Business equation:
Where,
Wt = unit pressure transmitted at any point in the pipe
P = superimposed load of traffic
Z = the slant height of the considered point from the load P
H = distance of the top of pipe from the surface of the fill.
The total load transmitted on a unit length of the pipe (Wt) can be determined by integrating the equation (8.11) over the projected area of the pipe.
Now the total per unit length of the pipe from the back fill as well as from traffic can be determined from the following formula:
where, t = thickness of pipe m metres.
Example 4:
A pipe of 80 cm diameter is buried in a trench of 120 cm and the back filling is done by saturated top soil. The top of the pipe is 2.0 m below the surface of the fill. The pipe crosses a road at right angle, which carries a vehicle whose loading (including impact) consists of two concentrated 1200 kg loads located at 2.0 m a part transverse to the roadway.
Determine the maximum vertical force extorted on the unit length of the pipe, in the following conditions:
(i) If the pipe is made of cast iron.
(ii) If the pipe is made of steel.
(iii) What will be the stree in stress pipe, if its thickness is 12 mm.
The thickness of the pipe may be neglected for calculating the external diameter of the pipe.
Solution:
Essay # 6. Temperature Stresses on Pipes:
If the pipes are laid over or above the ground they will be exposed to the atmospheric actions. Due to change in temperature, there will be change in their length also. This change of length, if prevented, will cause internal stresses due to temperature.
As Stress/Strain = E
Or Stress = Strain × E
= (E × L × α × t)/L = E.α.t
Where, E = Modulus of elasticity of the pipe material
α = Coefficient of linear thermal expansion of the pipe material
t = Change in temperature in °C
