EUROPEAN JOURNAL OF PHYSICS
High precision pressure measurement with a funnel
´ T Lopez-Arias, L M Gratton and S Oss
Physics Department, University of Trento, 38100 Povo (Trento), Italy E-mail: firstname.lastname@example.org, email@example.com and firstname.lastname@example.org
Received 21 June 2008, in ﬁnal form13 August 2008 Published 22 September 2008 Online at stacks.iop.org/EJP/29/1235
A simple experimental device for high precision differential pressure measurements is presented. Its working mechanism recalls that of a hydraulic press, where pressure is supplied by insufﬂating air under a funnel. As an application, we measure air pressure inside a soap bubble. The soap bubble is inﬂatedand connected to a funnel which is placed, upside down, in a container ﬁlled with distilled water, placed on a scale. Our method provides a theoretical precision for the pressure measurement of the order of 0.01 Pa. Beyond this, the advantage of this method relies on the simplicity of the materials used and on the opportunity to discuss, at an undergraduate level, basic concepts regarding allthose phenomena in which low or very low differential pressures are relevant. (Some ﬁgures in this article are in colour only in the electronic version)
We present a high precision pressure measurement apparatus made with very simple and available materials. The pressure range accessible to this system is limited to relatively low differential pressures, with an absolute valueof 300 Pa. Other apparatuses of comparable precision, such as differential low pressure transmitters, are not only expensive, but their working mechanisms are much more difﬁcult to explain in the classroom. As a simple application, we measure the excess pressure, P , between the pressure inside and outside a soap bubble1 . Soap ﬁlms and bubbles offer an inexpensive and attractive way to illustratemany facts of physics and concepts of mathematics at an undergraduate level . Besides surface tension, interference, colour, pressure, molecular forces and liquid surface properties are other topics
1 The idea of an apparatus suited to this aim came up in a laboratory for in-service high school teachers devoted to the study of minimal surfaces.
c 2008 IOPPublishing Ltd Printed in the UK
´ T Lopez-Arias et al
Figure 1. The differential pressure measurement apparatus. A ruler is placed close to the bubble to
provide a length calibration scale to measure its diameter by inspecting the pictures. An increase in the bubble’s pressure relates to the variation of the water level and to the scale’s reading.
for which bubbles offeran effective window for teaching. In particular, the measurement of the pressure inside a soap bubble is an alternative method to determine the surface tension of a given soap solution, using the Young–Laplace equation . In this kind of experiment, emphasis is put on the interpretation of surface tension in terms of the surface free energy, as opposed to the mechanical concept, based on forcesand which is mostly used in elementary physics textbooks . The measurement of pressure inside a soap bubble can be quite a challenging task, especially if high precision is required. Interesting considerations are made regarding pressure behaviour inside the bubble during inﬂation.
2. The apparatus
Our experimental set-up consists of a plastic tube connected, on one side, to a metalliccylinder and, on the other side, to a PVC kitchen funnel of internal and external diameters: Dint = (11.30 ± 0.01) cm and Dext = (11.60 ± 0.01) cm, respectively. A glass container of diameter D = (13.50 ± 0.01) cm is ﬁlled with a few centimetres of distilled water. The funnel is placed in the water in such a way that its straight rim (3 cm high) remains immersed during the experiment. This...