Viscous Pipe Flow Lab Report

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The City College of New York, CUNY *

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436

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Mechanical Engineering

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Dec 6, 2023

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Viscous Pipe Flow Mechanical Engineering Department The City College of New York ME 436 Aerothermal Fluids Laboratory Saif Allahabi Lab Report 1 2023-10-06

Abstract: Pipe flow refers to a flow that passes via a circular pipe, ducts, nozzles, etc. Internal flows known as pipes occur when a fluid is fully surrounded by solid surfaces. Because energy is needed to counteract the viscous force imposed by the pipe walls when a gas or liquid travels through one, there is a pressure loss in the fluid. Head loss or frictional loss is the term for the pressure loss brought on by a viscous force. This experiment's major goals were to examine various flow resistances in the pipe, measure pressure inside the pipe at various places, and calculate the flow rates of the venturi tube and pitot tube. Reynolds number, friction factor derived from the chart and from the formula, and velocity profile both empirically and theoretically are all discussed. We measured the pressure taps' separation and identified their positions in order to obtain our results. The static pressure within the pipe, also known as the gage pressure, and the dynamic pressure were calculated with the use of the manometer and pitot tube. We utilized 13v to generate a flow into the pipe. The motor's torque was then measured in order to assess uncertainty. Different characteristics, including the Reynold number, friction factors, and others, were calculated using formulae and real-world measurements. The results show that the flow is inviscid at the inlet, the pressure gradually rises as the flow develops, and occasionally the flow becomes laminar as the flow fully develops. At the venture tube point, the pressure suddenly increases as the area of the tube decreases. According to the previous graphs, as we travel farther away from the border zone, velocity rises. At the boundary region, velocity is lower because of viscosity. the Colebrook White formula, the Reynolds number, the viscous flow in a pipe, the head loss, the laminar flow, the turbulent flow, the flow rate, the venturi tube, the manometer, and the pitot tube

Introduction: We classify a fluid flow as internal whenever it is entirely contained by a surface. The fluid in this experiment is pipe flow since it is contained by a pipe. The frictional force produced by the pipe's boundary on the fluid causes a drop of pressure in the fluid when the fluid is injected into the pipe and the flow continues. Head loss is the term for this pressure loss. Major losses are those caused by friction, whereas small losses are those caused by fittings, etc. The total head loss is the sum of these two losses. The shear force created on the pipe wall when fluid comes into direct contact with it by the pipe's roughness and viscosity tends to generate the velocity profile. Our experiment aims to measure the fluid's flow rate and velocity as it passes through the pipe. We will use a set of equations created especially for this goal to do this. We can learn a lot about how fluid behaves within pipes by using these equations, and we can also learn more about how friction and pressure losses affect the flow dynamics. U mean = √ 2 ( d a d b ) 4 − 1 ( ∇ P Venturi ρ ) Where, d a is the pipe diameter and d b is the venturi tube diameter. We also calculate Q Venturi using the equation below: Q Venturi = U mean ∗ Area The velocity through the venturi is: u ( r ) = √ 2 ∆P ρ To determine Q Pitot , we need to integrate the velocity profile of the tube, which is given by the integral equation below: Q Pitot = 2 π ∫ r = 0 r = wall u ∗ rdr The theoretical velocity is given by, Q theoretical ( r ) = u max ( 1 − r 2 R 2 ) 1 n

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Experimental Setup and Procedure: These are the components of the lab's experimental setup. Viscous Pipe: This lab's most important tool. We have a row of straws covering the full inner diameter at the pipe's entry. The air may be laminated thanks to these pipes. The Pitot tube is our next tool, and it enables us to construct velocity profiles by measuring pressures at various heights. The venturi meter is the next item, and it may be used to calculate velocity using the continuity equation. The blower, which creates flow in the pipe, is located at the very end. We have inlets throughout the full length of the pipe that we can use to gauge the pressures in various regions of the pipe. A manometer is used to measure the pressures. The process is as listed below. Measuring is where we start. In order to graph the pressure vs location in our study, we must quantify the lengths between the inlets. In our reading, the sizes were reported as D1=145mm and D2=90mm, where D1 represents the pipe's diameter and D2 represents the venturi meter's diameter. In order to generate a flow speed that we could easily deal with, we set the blower voltage to 13V. Then, we set our dynamometer's calibration to zero. Using our manometer, we gauged the pressures at the pipe's inlets. Using the manometer and pitot tube, we also recorded pressure readings at various heights.

Calculations:

Results: Viscous Pipe Experiment Table Tube # Edge to edge measurement between the tubes (inches) 1 12.7 (from edge of pipe to first tube) 2 15.5 3 24.1 4 27 5 23.8 6 23.5 7 24.2 8 24.2 9 (dynamic pressure tube) 22.8 10 13.1 11 (distance between 9 & 11) 35.7 12 6.2 13 10 14 21.75 Static pressure along the tube at 48hz Tube # P (H2O) 1 0.53 - 0.76 2 0.53 - 2.25

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3 0.53 - 2.26 4 0.53 - 2.29 5 0.53 - 2.32 6 0.53 - 2.32 7 0.53 - 2.32 8 0.53 - 2.34 9 (dynamic pressure tube) 10 0.48 - 2.35 11 0.48 - 2.36 12 0 - 2.7 13 0.22 - 2.28 Dynamic pressure at intervals of 0.5 at 45hz Interval P (H2O) 0 0.22 - 0.32 0.5 0.22 - 0.38 1 0.22 - 0.40 1.5 0.22 - 0.42 2 0.22 - 0.44 2.5 0.22 - 0.44 3 0.22 - 0.45 3.5 0.22 - 0.46 4 0.22 - 0.44 4.5 0.22 - 0.4

Static pressure along the tube at 45hz Tube # P (H2O) 1 0.3 - 0.5 2 0.3 - 1.82 3 0.3 - 1.82 4 0.35 - 1.84 5 0.35 - 1.86 6 0.35 - 1.86 7 0.35 - 1.84 8 0.35 - 1.88 9 (dynamic pressure tube) 10 0.3 - 1.9 11 0.3 - 1.91 12 0.3 - 2.5 13 0.3 - 2.02 Dynamic pressure at intervals of 0.5 at 45 hz Interval P (H2O) 0 0.24 - 0.28 0.5 0.24 - 0.34 1 0.24 - 0.38 1.5 0.24 - 0.4 2 0.24 - 0.4

2.5 0.24 - 0.4 3 0.24 - 0.41 3.5 0.24 - 0.41 4 0.24 - 0.40 4.5 0.24 - 0.38

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Discussion of Results: After analyzing the data, we discovered that the pressure at the tube's entry starts off low, rises to a stable level, then spikes once more before falling down. Our findings show that as distance from the wall increases, pressure decreases and velocity increases. The velocity increases as one approaches the tube's core. The length of the pipe also affects how quickly the fluid flows since the walls slow the stream down. Conclusion: In conclusion, there are a variety of elements that determine how viscous flow behaves in a smooth pipe experiencing turbulent flow. One of the contributing reasons is head loss in various parts of the pipe. This results from the fact that pipes expand and contract as fluid passes through them. There is also the friction component, which contributes to the resistance the fluid experiences as it passes through the pipe. The fluid's own viscosity: thicker fluids flow more slowly. The length of the pipe and the fact that fluid movement is fully stopped at the pipe walls, however, play the biggest roles in this situation. Higher static pressure and no velocity result from this. There is dynamic pressure with some velocity in the pipe's middle. This is evident in both our findings and earlier theoretical investigations.

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MATLAB codes: clc clear all close all hinit=[.1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1]; hfinal=[.74 4 4.2 4.2 4.2 4.26 4.32 4.4 4.52 7.8 5.1]; location=[7.75 23.375 95.75 120.438 134.125 158.125 181.625 209.188 253.875 264.063 286.125]; voltage=13; rpm=[1131 1136 1101 1112 1099 1112 1103 1129 1101 1137]; hinitpress=[-.6 -.5 -.4 -.3 -.3 -.2 -.2 -.2 -.2 -.3 -.4 -.4 -.6 -.75].*0.0254; hinitpress2=[-.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6 -.6].*0.0254; hfinpress=[3.7 3.83 3.92 4.03 4.13 4.2 4.21 4.2 4.12 4.1 4.01 3.91 3.8 1.5].*0.0254; rad=[12.4 12 11.6 11.2 10.8 10.4 10 9.6 9.2 8.8 8.4 8 7.6 7.2 6.8]; polar=[0 0.4 0.8 1.2 1.6 2 2.4].*0.0254; polarfull=[0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 5.2]*0.0254; %part a %i delh=hfinal-hinit; %ii delhm=delh.*.0254; %iii rho=1000; g=9.81; alpha=0.05; rhomdot=827/784; pressure=delhm.*rho.*g.*alpha.*rhomdot; %a-b figure; plot(location,pressure,'-r*'); xlabel({'Distance along the Pipe',('(in m)')});

ylabel({'Gage Pressure in the Pipe', ('(Pa)')}); title('Pressure vs Distance');delpvent=pressure(10)-pressure(9); %b-b da=.145; db=.09; umean=sqrt(((2*delpvent))/((da/db)^4)-1); %c flow=(pi*(db^2)/4)*umean; %using pitot tube delpitot=hfinpress-hinitpress2; delpressure=delpitot.*rho.*g.*alpha.*rhomdot;%%%%%%%%%%%%%%%%%%%%%%%% velocity=sqrt(2*delpressure); % THIS part % qpitot=2*pi*trapz(velocity(7:13).*polar,polar);%%%%%%%%%%%%%%%%%%%%%%% figure; plot(polar,velocity(7:13),'--*'); xlabel({'Radiuis',('(in m)')}); ylabel({'Velocity of the Fluid', ('(m/s)')}); title('Velocity From Pressure Profile'); >> %b delpvent=pressure(10)-pressure(9); %b-b da=.145; db=.09; umean=sqrt(((2*delpvent))/((da/db)^4)-1); %c flow=(pi*(db^2)/4)*umean; %using pitot tube delpitot=hfinpress-hinitpress2; delpressure=delpitot.*rho.*g.*alpha.*rhomdot;%%%%%%%%%%%%%%%%%%%%%%%% velocity=sqrt(2*delpressure); % THIS part % qpitot=2*pi*trapz(velocity(7:13).*polar,polar);%%%%%%%%%%%%%%%%%%%%%%%

figure; plot(polar,velocity(7:13),'--*'); xlabel({'Radiuis',('(in m)')}); ylabel({'Velocity of the Fluid', ('(m/s)')}); title('Velocity From Pressure Profile'); >> umax=max(velocity); utheory=umax*(1-(polar.^2)./((da/2)^2)^(1/2)); figure; plot(polar,velocity(7:13),'--*'); hold on plot(polar,utheory,'-ro'); legend('Velocity from Pressure','Velocity From Theory','location','southwest'); xlabel({'Radiuis',('(in m)')}); ylabel({'Velocity of the Fluid', ('(m/s)')}); title('Velocity from Pressure and Theory'); figure; plot(polar,utheory,'-ro'); xlabel({'Radiuis',('(in m)')}); ylabel({'Velocity of the Fluid Theoretical', ('(m/s)')}); title('Velocity vs Pressure with Theory'); figure;%%% pressure profile plot plot(delpressure,polarfull,'-g*'); xlabel({'Pressure',('(in Pa)')}); ylabel({'Polar Distance', ('(in m)')});

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