More than a pipe dream: uncovering mechanisms of vascular lumen formation

Blood vessel formation starts early during embryonic development, around day 7. In the extraembryonic yolk sac, mesodermal precursor cells called hemangioblast proliferate and differentiate into angioblast. Angioblasts express vascular endothelial growth factor receptor 2 or VEGFR2, which binds VEGF-A, a proangiogenic factor, guiding blood vessel formation. VEGF signaling promotes angioblasts to form a blood island in the developing embryo. Angioblasts further differentiate, giving rise to...

The development of the vascular system in a fetus is a complex and intricate process that begins as early as 15 to 16 days post-conception. This process starts outside the embryo, specifically in the mesoderm of the yolk sac, chorion, and connecting stalk. Approximately two days later, the formation of blood vessels occurs within the embryo itself.
The initial formation of this system is facilitated by the small amount of yolk present in the ovum and yolk sac. Blood vessels originate from...

Laminar flow represents a smooth, orderly fluid motion where particles move along parallel paths, resulting in minimal mixing between layers. Streamlined particle paths characterize this flow regime and occur under conditions where viscous forces dominate over inertial forces. The distinction between laminar, transitional, and turbulent flow is primarily determined by the Reynolds number, a dimensionless quantity calculated as:

When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe's cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe's length.
The distance to reach a fully developed flow is called the entrance length and depends on the flow...

Pipe flow refers to the movement of fluids within fully enclosed conduits, typically cylindrical in shape, such as water pipes or hydraulic hoses. These conduits are designed to withstand high-pressure gradients that drive fluid movement, contrasting with open-channel flows, where gravity is the primary driving force. Rectangular conduits, like air conditioning and heating ducts, generally operate at lower pressures and are less suited for high-pressure applications.
The classification of fluid...

Understanding fluid flow behavior through pipes is critical in fluid mechanics, especially in applications like oil transportation through pipelines. Hagen-Poiseuille's law provides an exact solution derived from the Navier-Stokes equations for steady, incompressible, and laminar flow within a circular pipe. Hagen-Poiseuille's law helps determine the necessary pressure drop across a pipeline section by determining parameters like pipe length, radius, oil viscosity, and the desired volumetric...