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Nature of Flow of a Liquid
Published in Wilmer W Nichols, Michael F O'Rourke, Elazer R Edelman, Charalambos Vlachopoulos, McDonald's Blood Flow in Arteries, 2022
The first published experimental work indicating that liquid flow is proportional to the fourth power of the radius was due to Hagen in 1839. He used brass tubes of a similar size to those of Girard; however, the results were not very accurate. The exponent of the radius derived from his results was actually 4.12, and he assumed that the real value was probably 4.0. Jean Louis Poiseuille (1799–1869) published his first results in 1842, although no full paper was published until 1846 (Poiseuille, 1846). Original biographical information on Poiseuille’s life is somewhat scarce. Brillouin (1930), Joly (1968), Pappenheimer (1978) and more recently Sutera and Skalak (1993) summarize most of the known information. Due to Hagen’s priority of publication, some references use the name “Hagen–Poiseuille equation”. Poiseuille’s work, however, was much more detailed and precise (Joly, 1968; Sutera and Skalak, 1993), and therefore it is fair to name it Poiseuille’s equation.
Fluids and Flow
Published in Sarah Armstrong, Barry Clifton, Lionel Davis, Primary FRCA in a Box, 2019
Sarah Armstrong, Barry Clifton, Lionel Davis
Rate of laminar flow is given by the Hagen-Poiseuille equation where P is the pressure difference across the tube, d is the diameter of the tube, r is the radius of the tube, η is the viscosity of the fluid and l is the length of the tube
Flow
Published in Lara Wijayasiri, Kate McCombe, Paul Hatton, David Bogod, The Primary FRCA Structured Oral Examination Study Guide 1, 2017
Lara Wijayasiri, Kate McCombe, Paul Hatton, David Bogod
Hagen–Poiseuille equation is used to calculate laminar flow: Where: π = Pi (mathematical constant – the ratio of any circle’s circumference to its diameter)ΔP = Pressure dropr = RadiusL = Length of tuben = Viscosity of fluid
XEN Implant for Glaucoma Treatment: A Review of the Literature
Published in Seminars in Ophthalmology, 2019
Aikaterini Chatzara, Irini Chronopoulou, George Theodossiadis, Panagiotis Theodossiadis, Irini Chatziralli
The XEN gel stent or XEN implant (Allergan, Dublin, Ireland) bypasses the normal route of aqueous humor outflow and reduces IOP though subconjunctival filtration. It is a biocompatible gelatin stent cross-linked with glutaraldehyde, which is inserted ab interno from the anterior chamber into the subconjunctival space and does not cause foreign body reaction while sustains its potency, as it is supported by human and non-human preclinical testing.12,13 There are three models, each 6 mm in length, but with different inner diameters of 140, 63 and 45 μm. The different diameters of the stents are designed in adherence to Hagen‒Poiseuille equation, so as to regulate accordingly outflow resistance.12 Assuming laminar flow of a non-compressible fluid, the outflow resistance and therefore pressure differential increases linearly in relation to the length of the tube and decreases to the fourth power of the lumen radius. A longer and thinner tube will provide more resistance to flow than a shorter and wider tube. This equation was applied as the principle of XEN implant.14 Specifically, it is known that aqueous humor production occurs at a rate of 2‒3 μL/min. In order to prevent hypotony, a device would need to create approximately 5 mm Hg of steady-state pressure at this rate, which can be thought of as the pressure difference between the two ends of a tube. If the length of the tube is set at 6 mm, a lumen of 45 μm would provide a steady-state pressure of approximately 6‒8 mm Hg at 2‒2.5 μL/min as calculated by the Hagen‒Poiseuille equation.14 As far as flow rate is concerned, at 5 mm Hg, the flow rate through this implant was measured at 1.2 μL/min. This is less than that of aqueous humor production and therefore theoretically protects against hypotony at average aqueous humor production.14
Assessment of early paediatric airway sequelae after using cuffed or uncuffed endotracheal tubes with ultrasound and flexible endoscopy
Published in Egyptian Journal of Anaesthesia, 2023
Mohammed Nassef Elsayed, Ahmed Mohammed Al-Attar, Emad Eldin Abd Elmonem Arida, Aliaa Rabia Abd Elaziz
In the present research, an obvious difference between the two groups as regard the inner diameter of the TT is demonstrated. Consecutively and according to Hagen – Poiseuille equation for laminar flow, it is expected that the work of breathing is higher in the CTT group than the UTT group. However, in the setting of general anaesthesia, the patient is already on a controlled mechanical ventilation which in turn alleviates the work of breathing resulting from the small inner diameter of the endotracheal tube [27].
XEN Gel Implant: a new surgical approach in glaucoma
Published in Expert Review of Medical Devices, 2018
Ankita Chaudhary, Lauriane Salinas, Jacopo Guidotti, André Mermoud, Kaweh Mansouri
The XEN GEL Implant (Allergan Inc., CA, USA) is a 6-mm tube of collagen-derived gelatin cross-linked with glutaraldehyde, making it permanent and non-degrading, with no foreign body reaction (Figure 1). It comes preloaded in an injector and is implanted ab-interno, creating a drainage pathway between the AC and subconjunctival space. The procedure is often augmented with subconjunctival injection of MMC (off-label use). Long-term animal studies have shown the Xen Gel Implant structure to be stable over several years [33]. It hydrates on contact with water within 1–2 min, bending and conforming to tissue, reducing the risk of erosion. Microforce testing has shown the XEN Gel Implant to be more than 100 times as flexible as a typical silicone shunt tube [34]. Although initially produced with three different lumen diameters, the tube with the 45-μm lumen size is the only device now recommended for implantation by the manufacturer. This lumen size was chosen in an effort to design a device with the necessary dimensions to prevent postoperative hypotony by the primary flow resistance of the tube itself [35]. The tube length of 6 mm was identified as the ideal length for passage ab-interno from the trabecular meshwork to the subconjunctival space at an optimal distance from the limbus. The Hagen–Poiseuille equation was then used to calculate the required internal dimensions of a tube that would prevent hypotony at average aqueous humor production of 2–3 μl/min by providing a steady-state pressure of approximately 6–8 mmHg. A longer thinner tube will provide more resistance to flow than a shorter and wider tube. This equation was used as the principle of XEN Gel Implant [35]. Implants of larger lumen size rely on conjunctival resistance to prevent hypotony, and as conjunctival resistance is low in the immediate postoperative period, the risk of hypotony with larger lumen tube stents is greatest at that time. The XEN Gel Implant received CE mark in 2011 and US FDA approval in 2016.