Velocity Of Flow 3z3x29

Minimum Velocity of Flow • In order to keep the solid matters in suspended form, a certain minimum velocity of flow is required, otherwise the solid particles will settle in the sewer, resulting in its clogging. • Such a minimum velocity is known as self cleansing velocity. • A self cleansing velocity may be defined as that velocity at which the solid particles will remain in suspension, without settling at the bottom of the sewer. • Also it is that velocity at which even the scour of the deposited particles of a given size will take place.

Shield’s Expression for Self Cleansing Velocity • The self cleansing property of the sewage depends upon the scouring action of the flowing sewage.

• According to Shield, the velocity required to transport water-borne solids is the self cleansing velocity.

• Consider a layer of sediment of a unit length, unit width and thickness t, deposited at the invert of the sewer. Let the slope of the sewer be α. The drag force or the intensity of tractive force (τ) excreted by the flowing water on a channel is given by the following equation……. τ = γw R S

Where… γw = Unit weight of water at the prevailing temperature R = Hydraulic radius of the filled section S = Slope of the invert or head loss per unit length of sewer

The submerged unit weight of the sediment is given by…..

Where… γsub = Submerged Unit weight of water at the prevailing temperature Gs = Specific gravity of the sediment e = Void ratio of the sediment deposit

So, weight of the sediment of unit length and unit weight is given by…

The Frictional resistance R is given by…. When the sediment is just on the point of sliding…. τ = R….. Hence….. Putting (1-n) sin α = k, where k is the important characteristic of the sediment, to be determined by the experiments, we get…..

For single grains, the volume per unit area t becomes the function of the diameter of the grains ds as an inverse measure of the surface area of the individual grains exposed to the drag or friction.

Now, from Chezy’s Equation…… Denoting V = Vs as self cleansing velocity, and substituting the value of S, we get…..

To find the value of Chezy’s Constant, use Darcy – Weisbatch formula for head loss HL…..

For Circular pipes running full…… , R = D / 4

Where… Vs = Self Cleansing velocity β = Characteristics of the solids flowing in the sewage, in suspension f = Darcy – Weisbatch friction factor = 0.03 Gs = Specific Gravity of the sediments, ranging from 2.65 for inorganic sediments to 1.2 for organic sediments g = Gravitational acceleration constant ds = Diameter of the solid particles

Maximum Velocity of Flow • There is also some upper limit for the flow velocity so that the interior surface of the sewer is not damaged due to wear. • At higher velocity, the flow becomes turbulent, resulting in continuous abrasion of the interior surface of the sewer, by the suspended particles. • The maximum velocity at which no scouring action or abrasion takes place is called non scouring velocity. • It depends upon the material used for sewer construction. • Abrasion is maximum at the bottom surface because grit, sand etc. travel along the invert.

Hydraulic Elements of Circular Sewer • Circular cross section sewers are most commonly used due to several advantages like….. 1. Easy manufacturing 2. Gives maximum HMD when running full and half full 3. Most economical 4. Uniform curvature all round and provides minimum chances for sedimentation

Circular Section running full……

Circular Section running partially full……

Let….. a = area of cross section p = wetted perimeter r = h.m.d v = velocity of flow Central angle is given by…… 1 𝑑 Cos 𝜃 = 1 − 2 2

𝐷

1. Depth

2. Area or

3. Wetted Perimeter

4. H.M.D or

5. Velocity of Flow n = Manning’s rugosity coefficient

6. Discharge q = a*v ….. , taking N/n = 1, we have….

For variable values of N/n, we get…

The figure shows the variation of the ratios of these hydraulic elements with the depth ratio d/D.

Partial Depth Self Cleansing Flow • Sewers flowing between 0.5 and 0.8 full need not to be placed on steeper grades to be self cleansing as sewers running full. • This is so because the velocity and discharge are functions of tractive force intensity which depends upon friction coefficient as well as the velocity. • Assuming that equality of tractive force intensity implies equality of cleaning………..

Example 1: A stone ware sewer, 30 cm in diameter is laid at a gradient of 1 in 100. Using N=0.013 in Manning’s formula, calculate the velocity, discharge and Chezy’s coefficient when sewer is running full.

Example 2: Find the minimum velocity and gradient required to transport coarse sand through a sewer of 60 cm dia with sand particles of 1 mm dia and specific gravity 2.66. assume β = 0.06 and f = 0.02. Assume the sewer to run half full. Take N = 0.012