To characterize the pressure-flow relationship of tubes used for semi-occluded tract, voice therapy, voice training, flow resistance, pressure drop, oral pressure . Individual flow rate and pressure data points were found by. Considering the Flow to be Laminar and through a Circular pipe the relationship between pressure drop and flow rate in a given length will be given by HAGEN. In addition to basic treatment information, such as actual flow rates, elapsed relationship exists between flow rate and pressure drop for flow through a tube.Poiseuille's Law - Pressure Difference, Volume Flow Rate, Fluid Power Physics Problems
The flow was driven by a compressed air source connected to a flow line. In line with the flow was a pressure regulator Fairchildmaintaining Leading from the flow meter was flexible PVC tubing, connected to a A flow straightener was constructed at the entrance of the upstream pipe to assure laminar flow.
A pressure tap was placed approximately 2 cm upstream of the tube entrance and pressure was measured using a silicone pressure transducer Omega PXD. Tubes were secured to the end of the setup via a custom fixture, consisting of a circular piece of 9.
Pressure-flow measurements were obtained for a wide range of tube diameters and lengths.
fluid dynamics - Does pressure drop across pipe affect flow rate? - Physics Stack Exchange
Standard round plastic tubing Evergreen Scale Models was used. Tube inner diameters that were studied included 1. Each of these tubes was cut to lengths of 3, 6, 12, and 24 cm. The tubes were tested in randomized order by diameter and then by length.
The experiments were repeated 3 times in different random orders. Flow was ramped up in increments of either 0.
Smaller diameters required higher resolution in order to obtain a sufficient number of data points, as the pressure reached its upper limit at low flows. Total Fluid Energy Daniel Bernoulli, a Swiss mathematician and physicist, theorized that the total energy of a fluid remains constant along a streamline assuming no work is done on or by the fluid and no heat is transferred into or out of the fluid. The total energy of the fluid is the sum of the energy the fluid possesses due to its elevation elevation headvelocity velocity headand static pressure pressure head.
The energy loss, or head loss, is seen as some heat lost from the fluid, vibration of the piping, or noise generated by the fluid flow. Between two points, the Bernoulli Equation can be expressed as: In other words, the upstream location can be at a lower or higher elevation than the downstream location.
If the fluid is flowing up to a higher elevation, this energy conversion will act to decrease the static pressure. If the fluid flows down to a lower elevation, the change in elevation head will act to increase the static pressure. Conversely, if the fluid is flowing down hill from an elevation of 75 ft to 25 ft, the result would be negative and there will be a The velocities recorded upstream of the lesion are displayed for one cardiac cycle in Figures 2 and 3.
Single-cardiac cycle velocity recorded upstream of the lesion, pre-treatment. The single cardiac cycle ends at 0. Single-cardiac cycle velocity recorded upstream of the lesion, post-treatment. The governing differential equations are: To simplify the expressions, tensor notation has been used. The subscript t refers to turbulent quantities. This method has been shown to correctly capture very low Reynolds numbers transitional flows in the literature [ 50 - 59 ].
The blood viscosity was modeled with a non-Newtonian model described in [ 9 ] as shown in Equation 7. The spatial discretization was performed in a sequence of increasingly refined stages wherein the elements were reduced in size until the results were independent of mesh. The mesh was deployed finely near the artery wall where large gradients of velocity exist.
A side view and end view of the mesh are shown in Figure 4. Side view, end view, and internal views of the computational mesh.
The figure also shows an internal view of the mesh with a callout that magnifies the mesh across the stenosis lumen. The magnification shows the refinement of elements in the near wall region. The final number of elements depended on the length of the lesion but were approximately 50, Similarly, the time step size was modified until results were independent of time step.
The final time step used for the calculations was 0. In total, three different calculations were made for each lesion.
One calculation was for laminar flow at peak systolic velocity. The second calculation was pulsatile four cardiac cycles using a laminar solver, and the third calculation was pulsatile four cardiac cycles where laminar-to-turbulent transition was included. A comparison between these three calculations will be provided later and it will be seen that they are in good agreement with each other. Results and Discussion The first set of results to be discussed is the pressure losses through the stenosis for the three calculation methods steady laminar, unsteady laminar, and unsteady transitional.
The comparison will be made at peak systole for the unsteady cases.
The Effect of Plaque Removal on Pressure Drop and Flow Rate through an Idealized Stenotic Lesion
Comparisons will be made both before and after the atherectomy treatment. The plaque was removed through the use of the Diamondback orbital atherectomy device Cardiovascular Systems, Inc.
We used a 2. The activation time was 30 seconds per pass, with a pause of 30 seconds in between passes. The atherectomy result was checked via angiogram, and the residual stenosis was measured with the IVUS. Table 1 shows a summary of the results for the pre-operative case. In the table, pressure drop through the lesion for the steady laminar, unsteady laminar, and unsteady transitional.