1. While researching fluid dynamics, you come across a reference to the dimensionless number called the Laplace number, given by the equation below.

2. The apparatus shown below is designed to measure the density of an unknown fluid (p2₂). The two sides of the device are separated by a movable, frictionless partition. The partition is attached to the immobile sidewalls of the device via springs (different spring constants) on either side. Before pouring fluid into the device, both springs are unstretched. The device has a rectangular cross-section and extends a width w into the page. Derive an expression for the unknown density p2 = f(p1, h₁, h₂, k₁, k2, Ax, g), where Ar is the displacement of the partition relative to its equilibrium location before the fluids are poured into the apparatus. h₁ P1 k₁ 5 P2 ли Ax k₂ h₂

the navier stokes equation  larger or smaller are the options

7.2 One-dimensional unsteady flow in a thin liquid layer is described by the equation du + u 6. Use a length scale, L, and a velocity scale, Vo, to nondimensionalize this equation. Obtain the dimensionless groups that characterize this flow.