EXAMPLE 6.1.3. HEAD LOSS USING DARCY WEISBACH FORMULA

Determine the discharge of water through a 2000-m length of 0.90-m diameter wood stave pipe if the head lost is 4m.

           

where:   L  = 2000m
             D  = 0.90m
             hf = 4m


The required, discharge, will be taken from velocity in the equation. However, the value of f is also dependent on the velocity, leaving two unknowns in the equation.

Pipe dia		Mean	Velocity	(V)	in Feet	per	Second
(in)	0.50	1.00	2.00	3.00	4.00	5.00	10.00	15.00	20.00
0.5	0.042	0.038	0.034	0.032	0.030	0.029	0.025	0.024	0.023
0.75	0.041	0.037	0.033	0.031	0.029	0.028	0.025	0.024	0.023
1	0.040	0.035	0.032	0.030	0.028	0.027	0.024	0.023	0.023
1.5	0.038	0.034	0.031	0.029	0.028	0.027	0.024	0.023	0.023
2	0.036	0.033	0.030	0.028	0.027	0.026	0.024	0.023	0.022
3	0.035	0.032	0.029	0.027	0.026	0.025	0.023	0.022	0.022
4	0.034	0.031	0.028	0.026	0.026	0.025	0.023	0.022	0.021
5	0.033	0.030	0.027	0.026	0.025	0.024	0.022	0.022	0.021
6	0.032	0.029	0.026	0.025	0.024	0.024	0.022	0.021	0.021
8	0.030	0.028	0.025	0.024	0.023	0.023	0.021	0.021	0.020
10	0.028	0.026	0.024	0.023	0.022	0.022	0.021	0.020	0.020
12	0.027	0.025	0.023	0.022	0.022	0.021	0.020	0.020	0.019
14	0.026	0.024	0.022	0.022	0.021	0.021	0.020	0.019	0.019
16	0.024	0.023	0.022	0.021	0.020	0.020	0.019	0.019	0.018
18	0.024	0.022	0.021	0.020	0.020	0.020	0.019	0.018	0.018
20	0.023	0.022	0.020	0.020	0.019	0.019	0.018	0.018	0.018
24	0.021	0.020	0.019	0.019	0.018	0.018	0.018	0.017	0.017
30	0.019	0.019	0.018	0.018	0.017	0.017	0.017	0.016	0.016
36	0.018	0.017	0.017	0.016	0.016	0.016	0.016	0.015	0.015
42	0.016	0.016	0.016	0.015	0.015	0.015	0.015	0.015	0.014
48	0.015	0.015	0.015	0.015	0.014	0.014	0.014	0.014	0.014
54	0.014	0.014	0.014	0.014	0.014	0.014	0.013	0.013	0.013
60	0.014	0.013	0.013	0.013	0.013	0.013	0.013	0.013	0.012
72	0.013	0.012	0.012	0.012	0.012	0.012	0.012	0.012	0.012
84	0.012	0.012	0.011	0.011	0.011	0.011	0.011	0.011	0.011

Assume a value of f. From the table, the range of f for 900mm diameter is 0.018 to 0.015. Take the average 0.016.

                
               
                       

               


Using this velocity, the value of f turns to be:

              

              f=0.0159    0.016 (so assumed f is correct)

So,    is also correct.  The discharge is then as follows:

          

             


RELATED TOPIC:

6.0. PIPES