6.6. MINOR LOSSES

Considering friction loss as the major loss of head in pipes, there are also some minor losses present. These minor losses affect the velocity of the flow, thus they become deviations of the velocity head. They come from various conditions:

1. Contraction
2. Enlargement
3. Gate
4. Bend
5. Change in direction
6. Obstructions

6.6.1. LOSS OF HEAD DUE TO CONTRACTION

Sudden contraction of the pipe size can cause head loss, in which it is equated as below:

                                  

where:    = head loss due to contraction
              =  empirical coefficient of contraction
            V   = velocity in the smaller pipe

Values of the coefficient Kc for sudden contraction (English units) are tabulated as follows. Interpolation is required for exact values.

VELOCITY IN SMALLER PIPE, V			RATIO OF	SMALLER	TO	LARGER	DIAMETER
	0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
2	0.49	0.49	0.48	0.45	0.42	0.38	0.28	0.18	0.07	0.03
5	0.48	0.48	0.47	0.44	0.41	0.37	0.28	0.18	0.09	0.04
10	0.47	0.46	0.45	0.43	0.40	0.36	0.28	0.18	0.10	0.04
20	0.44	0.43	0.42	0.40	0.37	0.33	0.27	0.19	0.11	0.05
40	0.38	0.36	0.35	0.33	0.31	0.29	0.25	0.20	0.13	0.06

*Values of the coefficient for sudden contractions will be much smaller.

A different case for sudden contraction is used for pipe entrances. The formula for the loss of head at pipe entrance is as follows:

                                  

where:  Cv = coefficient of velocity

ENTRANCE TO PIPE	Cv
Inward projecting	0.75
Square cornered	0.82
Slightly rounded	0.90
Bell mouth	0.95

EXAMPLE 6.6.1.1. EXAMPLE OF HEAD LOSS DUE TO SUDDEN CONTRACTION

EXAMPLE 6.6.1.2. EXAMPLE OF HEAD LOSS DUE TO SUDDEN CONTRACTION

6.6.2. LOSS OF HEAD DUE TO ENLARGEMENT

The enlargement of the pipe's cross section would cause the reduction in velocity. The loss of head due to sudden enlargement is given in the formula:

                                 

where: velocity head is taken from the smaller pipe;
           Ke is identified by Archer as:

                               

The case of sudden enlargement from pipe to a reservoir is a special case in which the ratio of diameters is taken as zero.




EXAMPLE 6.6.2.1. EXAMPLE OF HEAD LOSS DUE TO SUDDEN ENLARGEMENT
EXAMPLE 6.6.2.2. EXAMPLE OF HEAD LOSS DUE TO SUDDEN ENLARGEMENT

6.6.3. LOSS OF HEAD DUE TO OBSTRUCTIONS

6.6.3.1. GATES OR VALVES PARTIALLY CLOSED

Loss of head can also happen due to partially closed gates or valves. Head loss due to obstruction follows similar formula with the velocity head as the others:

                                

where:  V = mean velocity in the pipe

Diameter of valve, inches	Ratio of	opening	to	diameter	, d/D
	1/8	1/4	3/8	1/2	3/4	1
1/2	450	60	22	11	2.2	1
3/4	310	40	12	5.4	1.1	0.29
1	230	32	9	4.1	0.9	0.23
1-1/2	170	23	7.2	3.3	0.75	0.18
2	140	20	6.5	3	0.68	0.16
4	92	16	5.5	2.6	0.55	0.14
6	73	14	5.3	2.4	0.49	0.12
8	66	13	5.2	2.3	0.46	0.1
12	56	12	5.1	2.2	0.42	0.07

6.6.3.2. OBSTRUCTION IN A PIPE

For an obstruction inside the pipe, the head loss will be as follows:

                             

where:  A    = area of pipe
             a   = largest area of obstruction
            Cc   = coefficient of contraction
             V   = velocity of flow in pipe

6.6.4. LOSS OF HEAD DUE TO BENDS