Industrial standard Syringe Essay Example | Topics and Well Written Essays - 750 words

Industrial standard Syringe - Essay Example The present paper deals with a syringe’s low Reynolds number flow. This scenario presents itself in the slow regulated intravenous fusion of drugs and fluids in laboratories or hospitals. For instance, in indicator-dilution experiments, the common values for the Reynolds number are Re= 0.07 (50cc syringe at 1cc/min or Re= 0.015(10cc syringe at 0.1 cc/min). A calibrated infusion pump is often used in maintaining the rates of infusion at constants. In figure 1 the plunger is moving to the left in a cylinder; fluid is pumped through a hollow needle of a diameter that is often less than 3% of the cylinder’s diameter. Because of the geometry the fluid dynamics can be divided into 2 parts: the flow in the needle and the flow in the cylinder. Dagan, Weinbaum and Pfeffer [1] solved the flow in the needle (orifice). They concluded that the velocity profile is mostly Poiseuille, with end effects maintained at a length of just  ¼ the diameter of the needle. In the sections that follow we will examine the cylinder region, with the needle hole estimated by a sink. x’s partial differentiation is numerically solved using finite difference techniques, which result in an estimation for x at every grid point. In the middle way from all borders, standard difference equations are applied in the estimation of the partial derivatives. Close to the borders, multiple standard equations are required. These new difference equations, using both partials and values of x on the borders, were derived via the symbolic manipulation package, SMP. All the finite difference estimations applied are provided in Appendix A. The finite difference estimation produces results in a linear system of equations Ax = b, with dimension being 2500 for a basic 50 x 50 grid. Due to the fact that the boundary conditions are asymmetric and difference equations using known derivatives are used, the coefficient matrix A is