Question

two pipes of same length and the diameter 10cm and 20cm are connected in series. coefficient of friction is same for both pipe's. the diameter of an equivalent pipe is​

Answer 1

Given : Two pipes of same length and diameter 10 cm and 20 cm are connected in series .

coefficient of friction is same for both pipes.

To Find : The diameter of an equivalent pipe is

Solution:

Pipe 1

L₁ =  k

d₁  = 10 cm = 0.1 m

Pipe 2

L₂ =  k      as pipes of same length

d₂  = 20 cm = 0.2 m

Equivalent pipe

L  = k + k  = 2 k  ( connected in series )

d = ?

L/d⁵    = (L₁/d₁⁵)  + (L₂/d₂⁵)

=> 2k/d⁵  = (k/(0.1)⁵  +  k/(0.2)⁵

=> 2/d⁵   =  10⁵  + 10⁵/32

=> 2/d⁵ = 33 x 10⁵/32

=> d⁵  = 64/  33 x 10⁵

=> d  = 1.14 /10

d  = 0.114 m   or  11.4 cm

The diameter of an equivalent pipe is  11.4 cm

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