A realistic physiological pressure pulse can be represented

A realistic physiological pressure pulse can be represented as -dp/dx = a_0 + sigma_j = 1^n [a_j cos (2 pi jft) + b_j sin (2 pi jft)] Where j is the harmonic and f is the frequency in Hz (cycles per second. The solution procedure that is developed for a complex pulse exp (I omega t) = cos(omega t) + I sin(omega t) can be applied to an arbitrary Fourier series by adapting the solution for the different terms in the series and the change in Wormersley parameter as alpha_j = R[j 2 pi f rho/mu]^1/2 Determine the velocity profile for a pressure gradient represented by the equation (1) with the Wormsley number for the harmonics represented by eq. (2). Calculate the pressure and velocity profile if the pressure gradient is represented by only first two harmonics with f = 12 cycles/min, a_0 = 10^11 a_1 = 10^11 a_2 = 10^11, b_1 = 5 times 10^10, b_2 = 5 times 10^10.

Solution

in atmosheric science the pressure gradient is a physical quantity that describe which direction and at what rate the pressure changes the most rapidly around a particular location. the pressure gradient is a dimensional quantity expressed in units of pressure per unit length . mathematically it is obtained by appluing the del operator to a pressure function of position. the negative gradient of pressure is known as the force density.

in the petroleum geology and petrochemical sciences pertaining to oil wella and more specifically with in hydrostatic pressure, pressure gradients refer to the gradient of vertical pressure in a column of fluid with in a wellbore generally expressed in psi. this column of fluid is subject to the composed pressure gradient of the overlying fluids.