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Fall 2007 PHY126 Experiment 1

FLUID FLOW

Purpose:

The purpose of this laboratory is to study some aspects of viscous fluid flow and to see

demonstrations of fluid flow and statics, which can be interpreted by the Bernoulli

equation.

Part 1 - Viscous Fluid Flow:

According to Poiseuille's law, the viscous fluid flow Q (see text) through a tube is pro-

portional to the pressure difference P across the tube, so that P = RQ. The resistance to

flow is R = 8l /r4 where l is the tube length, r is the radius of the tube, and is the

fluid viscosity. The applicability of this law to water flow through glass capillary tubes isinvestigated here. The apparatus is very simple. It is sketched below.

The capillary is connected to the bottom of cups A and B. Cup A is positioned aheight h above cup B provided the capillary is horizontal, and that the water in cup A and

B is up to the overflow tubes, then the pressure difference on the capillary is just A = gh

( is the density of water). As water flows from A to B it will collect in the calibrated

beaker. By measuring the collection time, the flow rate Q can be computed. It is

important to keep adding water to cup A so that the water level stays at the top of the

overflow tube.

Procedure:

1. Connect the capillary tube to the cups. Add water to A and pinch the rubber con-

necting tubes until the air bubbles are removed - and water commences to flow.

2. You must time the water flow in order to relate the amount of water accumulated inthe beaker to flow rate Q. Do this as follows: Put the end of your finger over the hole

in cup A so that the water cannot flow through the capillary; empty the calibrated

beaker and get it set up; start the timer and remove your finger; add water to cup A as

needed to keep the level constant. Do this until a few minutes have elapsed and/or at

least 50 mlhave collected in the beaker.

State University of New York at StonyBrook

Cup A

Cup B

Overflow Tube

Calibrated Beaker

Capillary

Overflow Tube

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3. Take measurements on two different capillaries with 1 mm and 2 mm diameters. For

each tube, vary h to have at least 4 different values over the range from 5 cm to 30 cm.

4. For each tube, compute R = p/Q for each value of h.

5. Now compute R for each tube from the equation given above.

6. Next take the two tubes and hook them first in series and then in parallel, as shownbelow. Take new measurements for these combinations. Compute the effective resis

tance of the two combinations. You should find R(series) = R1+R2 and R(parallel) =

R1R2/(R,I+R2)

Questions:

1. Why is p = gh?

2. Within the estimated precision of your experiments, do you find: A) that R. is constant

for a given capillary?, B) that R(exp.) equals R(predicted)?, and C) that R(series) and

R(parallel) are given by the above formula? If not, give some possible systematic

uncertainties.

Part 2 - Bernoulli Effects, etc.:

In this part of the laboratory, you are asked to comment or make computations on theexhibits.

Exhibit I: A container of water has holes iii the sides. Why does the water from hole

A not go as far as the water from hole C? Give a quantitative explanation.

Series

R1 R2

R1

R2

Parallel

A

B

C

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Exhibit II: There is a Venturi tube apparatus for study. Give a qualitative description

and explanation of what you see.

Exhibit III: Hydraulic jacks are very useful for lifting heavy objects by application

of relatively small forces. Study the model jack setup in the laboratory. Push on both

sides so that you feel the jack action. What is the principle?

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