The study of the entrance region of microchannels and microdevices is limited, yet important, since the effect on the flow field and heat transfer mechanisms is significant. An experimental study has been carried out to explore the laminar hydrodynamic development length in the entrance region of adiabatic square microchannels. Flow field measurements are acquired through the use of microparticle image velocimetry (micro-PIV), a nonintrusive particle tracking and flow observation technique. With the application of micro-PIV, entrance length flow field data are obtained for three different microchannel hydraulic diameters of 500 μm, 200 μm, and 100 μm, all of which have cross-sectional aspect ratios of 1. The working fluid is distilled water, and velocity profile data are acquired over a laminar Reynolds number range from 0.5 to 200. The test-sections were designed as to provide a sharp-edged microchannel inlet from a very large reservoir at least 100 times wider and higher than the microchannel hydraulic diameter. Also, all microchannels have a length-to-diameter ratio of at least 100 to assure fully developed flow at the channel exit. The micro-PIV procedure is validated in the fully developed region with comparison to Navier–Stokes momentum equations. Good agreement was found with comparison to conventional entrance length correlations for ducts or parallel plates, depending on the Reynolds range, and minimal influence of dimensional scaling between the investigated microchannels was observed. New entrance length correlations are proposed, which account for both creeping and high laminar Reynolds number flows. These correlations are unique in predicting the entrance length in microchannels and will aid in the design of future microfluidic devices.

Since independence, Pakistan, like many other countries, has been facing the problem of the balance-of-payments deficit. A number of policies have been introduced during different periods for rapid and continuous growth in Pakistan’s exports. These policies, like import substitution, devaluation of the rupee in 1972, export finance schemes, tax concessions, delinking of the rupee from the U.S. dollar in 1982, etc., have helped in boosting its exports to some extent but not enough to stabilise its export earnings. The fluctuations in export earnings are known to have serious consequences. Specifically, unstable export earnings affect the investment decisions by hindering the continuous import of industrial raw materials. This, in turn, impedes the growth of the industrial sector. Moreover, it causes fluctuations in the GNP and promotes uncertainty in the economy. This uncertainty plays a decisive role in the private sector’s hesitation to invest in the large-scale manufacturing industries, thereby hampering the country’s overall development. Keeping in view the possibly serious consequences of export earnings instability, a study exploring its causes is in order. Concentration of exports on a few commodities and exporting to only a few markets is among the possible explanations of the current instability in Pakistan’s export earnings. Due to commodity concentration, the chances of offsetting the impact of adverse price movements in the international market are reduced. This commodity concentration is often associated with the concentration on primary products and is, therefore, the basis for a policy of diversification away from primary products. A diversification away from primary products and towards industrial goods is desirable for another reason, not central to this paper; and that is that the terms of trade argument which claims that the relative prices of the primary products have increased slowly relative to the prices of the manufactured goods in the international market.

An experimental investigation has been carried out to simulate the onset of gas entrainment phenomenon from a stratified region through branches located on a semicircular wall configuration, in close dimensional resemblance with a Canada Deuterium and Uranium (CANDU) header-feeder system. New experimental data for the onset of gas entrainment was developed during single and multiple discharge from an air/water stratified region over a wide range of Froude numbers (0 to 100), in order to thoroughly understand the onset of gas entrainment phenomenon. It was found that the critical height at the onset of gas entrainment (single or simultaneous) was a function of the corresponding Froude number of each branch, the vertical distance between the centerlines of the branches (for multiple discharge), the hydraulic resistance of the discharging lines, as well as the orientation of the branches and their diameter with respect to the main header. Concerning multiple discharge comparisons, at intermediate Fr values (1<Fr<10) the data deviates, however at higher Fr values (>10) there is convergence. The present data are necessary in validating future analytical and numerical models of the onset of gas entrainment for a curved geometry, particularly at low Froude numbers.

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The present investigation is focused on the onset phenomena from a stratified two-phase region through a single branch located on a semi-circular wall, resembling a circular reservoir of a CANDU header-feeder configuration. Two different models have been developed, over the whole range of branch Froude number, to predict the critical height at the onset of gas-entrainment. The results showed that there is both a maximum and a minimum physical limit of prediction, which depends on the branch size and configuration. Also, at a distinct range of Froude numbers within the physical limits, the predicted values of both models collaborated to the same values. The critical height corresponding to the onset of gas entrainment was found to be a function of the branch orientation and Froude number. Three different experimental data sets at branch orientation angles of zero, 45, and 90 degrees were used to validate the present models. A good concurrence was illustrated between the experimental and theoretical values.