An exhaust system is modeled as 9 ft of 0.125 ft diameter smooth pipe with the equivalent of (7) 90○ elbows and a muffler. The muffler has a measured loss coefficient of 8.5. The average flowrate is 0.1 ft3 /s with a fluid density of 0.003 slug/ft3 and a dynamic viscosity of 4.7 ⋅ 10−7 lbf-s/ft2 . (a) Determine the system resistance. (b) Compute the pressure drop through the exhaust system.

Solution:

The velocity of the exhaust air flow using continuity equation

   = 8.148 ft/s

Reynolds number,

    = 6501.06

As Re > 4000, the flow is turbulent.

Now calculating the friction factor of the flow,

  = 0.03519

Calculating the major head loss in the pipe

             = 2.614 ft

Calculating the minor head loss in the pipe

Here, n = number of elbows.

             = 10.936 ft

Now using Bernoulli equation between the entrance of the pipe and the exit of the pipe

Substitute , we get

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