An electric power plant draws 3.0 times 10^6 L/min of cooling water from the ocean through two...

Question:

An electric power plant draws {eq}\rm 3.0 \times 10^6\ L/min {/eq} of cooling water from the ocean through two parallel, 4.0-m-diameter pipes.

What is the water speed in each pipe? Express your answer with the appropriate units.

Liquid Flow Rate:

Whenever several specific pipes of the same cross-section are attached in parallel combination with a container that contains a liquid, then the parallel combination of pipes helps to increase the flow rate of the liquid. The value of the total flow rate from all pipes can be obtained by adding the flow rate of liquid through all the pipes.

Answer and Explanation: 1

We are given the following data:

  • The flow rate of water through two parallel pipes is {eq}Q = \left[ {3.0 \times {{10}^6}\;{\rm{L/min}}\; \times \left( {\dfrac{{\dfrac{1}{{60000}}\;{{\rm{m}}^{\rm{3}}}{\rm{/s}}}}{{1\;{\rm{L/min}}}}} \right)} \right] = 50\;{{\rm{m}}^{\rm{3}}}{\rm{/s}} {/eq}.
  • The diameter of the pipe is, {eq}d = 4.0\;{\rm{m}} {/eq}.


Since both pipes are attached in parallel combination from the ocean then the formula to calculate the water speed in each pipe is expressed as follows:

{eq}\begin{align*} \left( {\dfrac{1}{2}} \right)Q &= Av\\ Q &= 2\left( {\dfrac{\pi }{4}{d^2}} \right)v\\ Q &= \left( {\dfrac{\pi }{2}{d^2}} \right)v\\ v &= \dfrac{{2Q}}{{\pi {d^2}}} \end{align*} {/eq}

Here,

  • {eq}v {/eq} is the water speed in each pipe.
  • {eq}A {/eq} is the cross-sectional area of the pipe.


Substituting the values in the above formula, we get:

{eq}\begin{align*} v &= \dfrac{{2\left( {50\;{{\rm{m}}^{\rm{3}}}{\rm{/s}}} \right)}}{{\pi {{\left( {4.0\;{\rm{m}}} \right)}^2}}}\\ &\approx 1.99\;{\rm{m/s}} \end{align*} {/eq}


Thus, the water speed in each pipe is {eq}{\bf{1}}{\bf{.99}}\;{\bf{m/s}} {/eq}.


Learn more about this topic:

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Flow Rate: Definition & Equation

from

Chapter 16 / Lesson 10
18K

Learn all about flow rate. Understand what flow rate is and discover the flow rate equation. Learn the flow rate for a pipe and what conservation of fluid flow means.


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