Izmir Institute of Technology s1

Izmir Institute of Technology Mechanical Engineering Department

ME 202 Fluid Dynamics I

BERNOULLI’S EQUATION APPLIED TO A CONVERGENT-DIVERGENT PASSAGE

LAB: Mech. Eng. Laboratory Building

Research Assistants: Gamze GEDİZ İLİŞ Zeynep Elvan YILDIRIM

1 BERNOULLI’S EQUATION APPLIED TO A CONVERGENT- DIVERGENT PASSAGE

Object: This experiment demonstrates the use of a Pitot-static tube, and investigates the application of Bernoulli’s theorem to flow along a convergent-divergent passage.

Experimental Set up:

Figure 1. Arrangement of the Apparatus for an Experiment on Bernoulli’s Equation

A duct of rectangular section is fitted to the exit of the contraction which leads from the airbox, and liners placed along the inside wall of the duct produce a passage which contracts to a parallel throat and then expands to the original width. The shape of this convergent- divergent passage is indicated in Figure 1, from which it may be noted that the convergent portion is shorter than the divergent portion. Air is blown through the passage, and a probe may be traversed along the centre line to measure the distribution of total pressure P and static pressure p. This probe is a Pitot-static probe. Pressure tappings are connected from the airbox and from the Pitot-static probe to a multitube manometer.

2 Theory: The aim of the experiment is to measure the distribution of total pressure P and static pressure p along the duct and to compare these with the predictions of Bernoulli’s equation. Consider how the equation is applied to the present case. Figure 2 shows the duct as a stream tube.

Figure 2. Measurement of Total and Static Pressure According to Bernoulli’s equation the total pressure P, defined by (1) should be constant along this tube, provided the flow is steady and that the air is incompressible and inviscid. If Po denotes the total pressure in the airbox, then we should expect the measured value of P along the passage to be the same everywhere as Po, if Bernoulli’s theorem is valid for this motion. Now the total pressure P is measured with comparative ease by an open ended tube facing the flow. Figure 2 shows a streamline starting from the airbox, passing the duct, and arriving at the mouth of the Pitot tube. The motion is arrested at this point, so that in Equation (1) the local value of u is zero. The pressure recorded by the Pitot tube is therefore the local value of total pressure P. If Bernoulli’s equation applies along the whole length of the streamline from the airbox, then P should be the same everywhere as the initial total pressure Po. The value of Po may be found easily from a pressure tapping in the wall, since the air velocity in the box is so slight as to make the difference between total pressure and static pressure quite negligible. The variation of static pressure p may be measured by the static pressure tube. Figure 2 shows a further streamline emanating from the airbox and flowing close to the surface of the probe. Provided that the holes in the surface of the probe are placed far enough from the tip of the tube as to be unaffected by the disturbance in this locality (which means in practice about 6

3 tube diameters away from the tip) then the flow is undisturbed by the holes, which measure the undisturbed pressure, which is the static pressure, p. To compare the measured values of p with the results of calculations we must use the continuity equation as well as the Bernoulli equation. Taking the flow as one-dimensional, that is assuming the velocity over any chosen cross-section to be uniform over that section, then the continuity equation for incompressible flow gives the volume flow rate as:

Q = u.A =ut.At (2)

Results: Air temperature 22°C = 295 K Barometric pressure 1028 mb = 1.028 × 105 N/m2

Report:  Find the density of the air  Draw the distance (x) versus static pressure (p) and distance (x) versus total pressure (P) diagram along the duct.

 Draw the distance (x) versus dimensionless velocity (u/ut) diagram along the duct.  Do not forget to give your experiment table (if necessary) with your reports.  You can ask your questions via mail ([email protected] or; [email protected]) or by coming to our office (Çevre-Arge binası 2.kat).