# Question What is the maximum flow rate of air that may occur at laminar condition in a 4 in diameter pipe at an absolute pressure of $$30 \mathrm{psig}$$ and $$100^{\circ} \mathrm{F}$$ ? If the pressure is raised to $$60 \mathrm{psig}$$, what is the maximum flow rate ? If the temperature is raised to $$200^{\circ} \mathrm{F}$$, what is the maximum flow rate? Explain the differences in answers in terms of the physical mechanisms involved. Provide answers in base $$\mathrm{SI}$$ units.

Transcribed Image Text: What is the maximum flow rate of air that may occur at laminar condition in a 4 in diameter pipe at an absolute pressure of $$30 \mathrm{psig}$$ and $$100^{\circ} \mathrm{F}$$ ? If the pressure is raised to $$60 \mathrm{psig}$$, what is the maximum flow rate ? If the temperature is raised to $$200^{\circ} \mathrm{F}$$, what is the maximum flow rate? Explain the differences in answers in terms of the physical mechanisms involved. Provide answers in base $$\mathrm{SI}$$ units.
Transcribed Image Text: What is the maximum flow rate of air that may occur at laminar condition in a 4 in diameter pipe at an absolute pressure of $$30 \mathrm{psig}$$ and $$100^{\circ} \mathrm{F}$$ ? If the pressure is raised to $$60 \mathrm{psig}$$, what is the maximum flow rate ? If the temperature is raised to $$200^{\circ} \mathrm{F}$$, what is the maximum flow rate? Explain the differences in answers in terms of the physical mechanisms involved. Provide answers in base $$\mathrm{SI}$$ units.
&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/2Step 1:Given:Diameter of the pipe&#160;(D)&#160;is&#160;$$\mathrm{{4}}$$&#160;in..Absolute pressure&#160;(p)&#160;is&#160;$$\mathrm{{30}}$$&#160;&#160;psia.Absolute temperature&#160;(T)&#160;is&#160;100&#176;FExplanation:Please refer to solution in this step.Step2/2Step 2 : Take the gas constant of the air to be&#160;1716&#8201;lbf&#8901;ft/slug&#8901;&#176;R.&#160;&#160;R=1716&#8201;lbf&#8901;ft/slug&#8901;&#176;RUsing the ideal gas law, calculate the density of the air&#160;(&#961;).&#8194;&#160;&#961;=pRT=30&#160;psia(1716&#8201;lbf&#8901;ft/slug&#8901;&#176;R)(100&#176;F)=4320&#8201;lbf/ft2(1716&#8201;lbf&#8901;ft/slug&#8901;&#176;R)(560&#176;R)&#8194;&#160;=0.0045&#8201;slug/ft3=0.0045&#8201;lbf&#8901;s2/ft4For the maximum laminar flow, the critical value of the Reynolds number is 2300.For temperature at&#160;100&#176;F, take the viscosity of the air to be&#160;3.94&#215;10&#8722;7&#8201;lbf&#8901;s/ft2.&#160;&#160;&#956;=3.94&#215;10&#8722;7&#8201;lbf&#8901;s/ft2Calculate the maximum velocity of the air&#160;(V).&#8194;&#160;Re=&#961;VD&#956;&#8194;&#160;V=&#956;Re&#961;D=(3.94&#215;10&#8722;7&#8201;lbf&#8901;s/ft2)(2300)(0.0045&#8201;lbf&#8901;s2/ft4)(4&#8201;in.&#215;1&#8201;ft12&#8201;in.)=0.605&#8201;ft/sCalculate the maximum flow rate of air&#160;(m&#729;).&#8194;&#160;m&#729;=&#961;VA=&#961;V(&#960;D24)=(0.009&#8201;slug/ft3)(0.302&#8201;ft/s)[&#960;(4&#8201;in.&#215;1&#8201;ft12&#8201 ... See the full answer