Lab Section Date. ME4751 Air Flow Rate Measurement

Transcription

1 Name Lab Section Date ME4751 Air Flow Rate Measurement Objective The objective of this experiment is to determine the volumetric flow rate of air flowing through a pipe using a Pitot-static tube and a laminar flow meter. The velocity at several axial locations is measured by traversing the Pitot-static tube along the radius of the pipe and the resulting velocity profile is used to calculate the air flow rate. A laminar flow meter attached at the end of the flow system is used to validate the result from the Pitot-static tube method. Experimental Set-UP The apparatus for this experiment is shown in the Figure 1. It is consisted of a long 4-in ID plastic pipe and a blower to induce the air flow. A bellmouth mounted at the pipe inlet and a honey-comb ensures a uniform velocity profile at the entrance. Pitot-static tube traversing stations are located at various axial locations along the pipe. A laminar flow meter located downstream of the air blower is used to measure the flow rate so as to compare to the flow rate obtained by the Pitot-static tube traverse method. Figure 1. Air Flow Rate Measurement Set-up

2 Pitot-static Tube Referring to Figure 2, the tip of the Pitot-static tube is to be oriented into the flow such that the axis is parallel to the incident fluid velocity. The flow entering the Pitot-static tube is decelerated to zero velocity resulting in an increased pressure due to dynamic pressure within the hollow tube that is above the outside static pressure. This pressure is called the total or stagnation pressure. The port in the sidewall of the tube, which is perpendicular to the velocity direction, is subject to the local static pressure. Connection to a manometer facilitates measurement of the dynamic pressure and the flow velocity at the selected location in the flow field. Let the velocity and the static pressure of air before entering the Pitot-static tube are V 1 and, respectively. The conditions within the tube where the velocity has been decelerated to zero are denoted with a subscript 2. Application of energy equation between the upstream point 1 and the point 2 yields the Bernoulli s equation, (1) If the tube is oriented horizontally Z 1 =Z 2. The fluid velocity at the total pressure port is zero, v 2 =0. Thus the upstream velocity v 1 is given by (2) where the air density at both locations is assumed to be constant. An inclined manometer is used to measure the pressure difference (p 2 -p 1 ); (3) Measurement of the pressure difference along with determination of the fluid density allows one to determine the local flow velocity. With sufficient number of local velocity measurements across the cross section, the flow rate may then be determined by integration. (4) Suppose v i is the local air velocity at the radius r i and v i+1 is the local velocity at the radius r i+1 (Figure 3). Then the air flow rate through a small area between the radii r i and r i+1 is 0.5 (5) Total volume flow rate is simply the summation of all flows covering from r 1 =0 to r n+1 =2 inch; (6)

3 The local velocity v i is obtained by combining Eqs. (2) and (3) and is given by (ft/s) (7) where the manometer reading h i measured in inches of water must be converted to ft and g is the standard gravitational acceleration, ft/s 2. Static pressure port air flow 1 Total pressure port 2 Static pressure port to manometer Alignment guide Total pressure port to manometer Figure 2. Schematics of a Pitot-static tube v i+1 axis of the pipe v i r i r i+1 Figure 3. Measured velocities at adjacent radii

4 Laminar Flow Meter Figure 4 shows schematics of a laminar flow meter. It contains a large number of very small diameter pipes and the pressure drop across the tube bank is measured by a manometer. The principle of this instrument is that any flow through a small diameter pipe with a moderate pressure drop is a laminar flow. The advantage of laminar flow meter is that volume flow rate can be calculated analytically. N - small tubes with a diameter d Flow direction L P 1 p 2 Figure 4. Schematics of a Laminar Flow Meter The volume flow rate through a horizontal pipe with a diameter d and a length L subjected to pressure difference p=(p 1 p 2 ) is given by [1] (8) where μ is the dynamic viscosity of the fluid. Total volume flow rate is simply (9) where N is the total number of small pipes. For a given laminar flow meter, total volume flow rate depends only on the pressure difference and the fluid viscosity. The laminar flow meter used in the present experiment is calibrated to give Q=400 ft 3 /min of air flow rate when the pressure difference is 8 in-h 2 O. Laboratory Procedure 1. Install the Pitot-static tube at station 1 (nearest to the pipe inlet), where the velocity profile is expected to be nearly uniform. Make sure all manometers are leveled and zeroed. 2. Set the Pitot-static tube at the centerline of the pipe such that the tip of the tube is pointed into the flow and is parallel to the incident fluid velocity.

5 3. Turn on the blower and establish a constant flow rate. 4. Record the inclined manometer reading in Table 1. Move the Pitot-static tube in the upward direction to the next radial position in an increment of 0.25 inch up to 1.75 inch (therein performing a half-traverse); at each location record the manometer reading in Table Move the Pitot-tube to station 2 designated by your instructor, and repeat steps 5 and A spreadsheet program employs Eqs. (5)-(7) to calculate the volume flow rate at the selected section. It is assumed that the air temperature of air is 70 0 F and air properties are evaluated at that temperature. Note the air velocity at r=2.0 is equal to zero because of no slip condition at the solid wall. 7. Read the pressure drop across the laminar flow meter and calculate the volume flow rate. Compare with the results obtained by the velocity traverse method. Complete the spreadsheet. All flow rates should be identical in theory. 8. Plot velocity profiles at station 1 and station 2. Are the velocity profiles at station 1 and 2 as expected? 9. Attach the spreadsheet and the velocity plot to this report. Table 1. Pressure changes at selected radial locations Radial location, i Radius (inch) Station 1, p Inch H 2 O Station 2, p Inch H 2 O Not needed Not needed References 1. Fundamentals of Fluid Mechanics, 5 th Ed., Munson, Young and Okiishi, Wiley, 2006, pp 412.