What does the equivalent length of 200 mm pipe mean here?

Length whose friction loss equals the total loss: f Le/D1 = sum of K

How is the exit loss expressed in terms of V1^2/2g?

(0.64)^2 = 0.4096 since V2 = 0.64 V1

2076 Bhadra · 4 marks

Equivalent length of pipeline losses

Short answer

Sum of loss coefficients expressed in 200 mm pipe velocity heads is 51.04. Equivalent length of 200 mm pipe with f=0.02 is L_e = (51.04 × 0.2)/0.02 = 510.4 m.

A pipe line system consists of the following sources of head losses. (i) Entrance loss in 200 mm diameter (ii) Friction loss in 500 m of 200 mm diameter pipe with f = 0.02 (iii) Sudden expansion from 200 mm to 250 mm diameter (iv) Exit loss from 250 mm diameter pipe. Obtain the equivalent length of 200 mm diameter pipe with f = 0.02.

Idea. Express every loss in terms of the velocity head in the 200 mm pipe, $\dfrac{V_1^2}{2g}$ , and find the length of 200 mm pipe ( $f = 0.02$ ) that has the same total loss: $f\dfrac{L_e}{D_1} = \sum K$ .

Areas: $\dfrac{A_1}{A_2} = \left(\dfrac{200}{250}\right)^2 = 0.64$ , so $V_2 = 0.64V_1$ .

Loss	Expression	In terms of $V_1^2/2g$
(i) Entrance	$0.5\dfrac{V_1^2}{2g}$	0.5
(ii) Friction, 500 m of 200 mm	$f\dfrac{L}{D}\dfrac{V_1^2}{2g} = 0.02\left(\dfrac{500}{0.2}\right)\dfrac{V_1^2}{2g}$	50
(iii) Sudden expansion	$\dfrac{(V_1 - V_2)^2}{2g} = \left(1 - \dfrac{A_1}{A_2}\right)^2\dfrac{V_1^2}{2g}$	$(1 - 0.64)^2 = 0.1296$
(iv) Exit from 250 mm pipe	$\dfrac{V_2^2}{2g} = (0.64)^2\dfrac{V_1^2}{2g}$	0.4096
Total		51.0392

Equivalent length of 200 mm pipe:

f\frac{L_e}{D_1} = 51.0392 \;\Rightarrow\; L_e = \frac{51.0392\times 0.2}{0.02} = 510.39\ \text{m}

Answer: Equivalent length $\approx 510.4$ m of 200 mm pipe (with $f = 0.02$ ). The minor losses (entrance, expansion, exit) alone are equivalent to about 10.4 m of pipe.

✓ Answer checked by Claude Opus 5.5 (high effort)

Prandtl mixing length and sudden expansion loss · Hydraulics, chapter 1 · asked 2×
Equivalent roughness from head loss test · Hydraulics, chapter 1
Siphon with 90 mm pipe, number and length · Hydraulics, chapter 2
Pump power and pipe length with Colebrook · Hydraulics, chapter 2
Cast iron pipe size for given head loss · Hydraulics, chapter 2
Maximum length of pipe portion AB · Hydraulics, chapter 2
Head loss with enlarged central pipe length · Hydro Power, chapter 1
Head loss at sudden enlargement · Hydro Power, chapter 1
Friction pile length, 300 mm, 250 kN · Foundation Engineering, chapter 8
Discharge and head loss in horizontal pipe · Hydro Power, chapter 1

All Hydraulics chapter 2 questions →

Equivalent length of pipeline losses

Related questions