Can you help me solve this question? A rectangular plastic pipe transports a stream of 0.01 m³/s unknown fluid. The pipe is 200 mlong and has a cross sectional dimension of 16 cm × 8 cm. The kinematic viscosity of unknownfluid is 5.5x10 m?/s. Estimate the Darcy frictional factor (f).

Given Data: The discharge is Q = 0.01 m3/s. The length of the pipe is L = 200 m. The…

Answered: A rectangular plastic pipe transports a…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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A rectangular plastic pipe transports a stream of 0.01 m³/s unknown fluid. The pipe is 200 m
long and has a cross sectional dimension of 16 cm × 8 cm. The kinematic viscosity of unknown
fluid is 5.5x10 m?/s. Estimate the Darcy frictional factor (f).

Expert Solution

Step 1

Given Data:

The discharge is Q = 0.01 m³/s.
The length of the pipe is L = 200 m.
The cross-sectional dimension is $16 cm \times 8 cm$
The kinematic viscosity is $ν = 5.5 \times 10^{- 5} m^{2} / s$

The flow velocity can be determined as,

$\begin{array}{rcl} V & = & \frac{Q}{A} \\ = & \frac{0.01 m^{3} / s}{16 cm \times 8 cm \times \frac{10^{- 4} m^{2}}{1 {cm}^{2}}} \\ = & 0.78125 m / s \end{array}$

Step 2

The hydraulic diameter of the pipe can be determined as,

$\begin{array}{rcl} D_{H} & = & \frac{4 A}{P} \\ = & \frac{4 \times 16 cm \times 8 cm}{2 \times (16 cm + 8 cm)} \\ = & 10.67 cm \end{array}$

Where A is the area of cross-section and the P is the wetted perimeter.

The Reynold's number can be determined as,

$\begin{array}{rcl} R e & = & \frac{V D_{H}}{ν} \\ = & \frac{0.78125 m / s \times 10.67 cm \times \frac{1 m}{100 cm}}{5.5 \times 10^{- 5} m^{2} / s} \\ = & 1515.15 \end{array}$

As Reynold's number is less than 2000 the flow is laminar.

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