Module 6. Flow through pipes

Lesson 18

DETERMINATION OF PIPE DIAMETER, DETERMINATION OF DISCHARGE, FRICTION FACTOR, CRITICAL VELOCITY

18.1 Piping Systems

a. Pipes connected in series

Fig. 18.1 Pipes connected in series

b. Pipes connected in Parallel

Fig. 18.2 Pipes connected in parallel

18.2  Dupit’s Equation for Equivalent Pipe

Equivalent pipe

 If several pipes of different lengths and diameter are connected in series, it can be replaced by single pipe called as equivalent pipe. This equivalent pipe of same diameter will have the same loss head and discharge which several pipes connected in series will have.

Fig. 18.3 Pipes of different lengths and diameters connected in series

Equivalent diameter

 The uniform diameter of the equivalent pipe is the equivalent diameter series or compound pipe.

Fig. 18.4 Equivalent pipe 

Equivalent length

The length of equivalent pipe which has the same head loss & discharge that of series or compound pipe.

Assumption for analysis

 Neglect the minor losses (frictional loss) and consider only the major head losses (friction loss) since h_minor << h_major

……… (iv)

On equating (iii) & (iv):

……… (v)

Eq. (v) is known as Dupit’s eq. for equivalent pipe.

Case1. Sometimes length of equivalent pipe is taken to be equal to the length of compound pipe i.e.

Le = L₁+ L₂+ L₃+ L₄+……….

In such cases diameter of equivalent pipe D_eq, can be calculated from Dupit’s equation.

Case2. Sometimes value of equivalent diameter is given & length of equivalent pipe requires replace compound pipe has to be determined by Dupit’s equation.

18.3 Numericals

Q 1. Three pipes are connected in series

Pipe	Length (m)	Diameter (cm)
l1	1000	50
l2	750	40
l3	500	30

(a) Calculate equivalent diameter considering the length equivalent pipe to be equal in that of compound pipe.

(b) Determine the length of equivalent pipe for an equivalent diameter of 40 cm.

Solution

(a)

(b)

Q 2. Consider pipe 1, 2, 3 connected in series of length l_1, l_2, l₃ respectively. D_1, D_2, D₃ with a diameter of pipe 1, 2, 3.

Pipe	Length (m)	Diameter (cm)
l1	1500	60
l2	750	50
l3	450	40

(a) Determine the eq. length for an eq. diameter of 50 cm.

(b) Determine the eq. diameter if the length of eq. pipe is equal to the length of compound pipe.

Solution

(a)

(b)