Question

A compound piping system consists of 1700 m of 50 cm, 1250m of 40 cm and 650 m of 30 cm pipes of the same material connected in series. I) what is the equivalent length of a 40 cm pipe of the same material? ii) what is the equivalent size of a pipe 3600 m long? iii) if the three pipes are in parallel, what is the equivalent length of a 50 cm dia pipe?

Answer 1

Sure, I can help you with that.

I) The equivalent length of a 40 cm pipe of the same material is given by the following equation:

L

eq

​

=∑

i=1

n

​

L

i

​

D

e

​

D

i

​

​

where:

L

eq

​

is the equivalent length of the pipe

L

i

​

is the length of the $i$th pipe

D

i

​

is the diameter of the $i$th pipe

D

e

​

is the diameter of the equivalent pipe

Substituting the given values into the equation, we get:

L

eq

​

=1700

40

50

​

+1250

40

40

​

+650

40

30

​

=2375 m

II) The equivalent size of a pipe 3600 m long is given by the following equation:

D

eq

​

=

n

1

​

∑

i=1

n

​

L

i

​

D

i

2

​

​

where:

D

eq

​

is the diameter of the equivalent pipe

L

i

​

is the length of the $i$th pipe

D

i

​

is the diameter of the $i$th pipe

n is the number of pipes

Substituting the given values into the equation, we get:

D

eq

​

=

3

1

​

(1700×50

2

+1250×40

2

+650×30

2

)

​

=42.8 cm

III) If the three pipes are in parallel, the equivalent length of a 50 cm dia pipe is given by the following equation:

L

eq

​

=

∑

i=1

n

​

L

i

​

1

​

D

i

​

D

e

​

​

1

​

where:

L

eq

​

is the equivalent length of the pipe

L

i

​

is the length of the $i$th pipe

D

i

​

is the diameter of the $i$th pipe

D

e

​

is the diameter of the equivalent pipe

Substituting the given values into the equation, we get:

L

eq

​

=

1700

1

​

50

50

​

+

1250

1

​

40

50

​

+

650

1

​

30

50

​

1

​

=1200 m

Step-by-step explanation: