# Pressure and velocity relationship in fluids electrolytes

### Fluids | Physics | Science | Khan Academy

Learn more about pressure, buoyant force, and flowing fluid so you can Finding height of fluid in a barometer Volume flow rate and equation of continuity. the velocity vector. The vorticity is twice the local angular velocity (rate of rotation) of the fluid. .. Dimensionless equation relating the pressure gradient in the tangential direction metals, and salt water or electrolytes. The concept behind. K Vη P [6] where V is the superficial velocity (the average velocity inside the porous media), P is the pressure gradient and η is the fluid viscosity. To find the through-plane and in-plane permeability Equation (7) and (8) should be solved with.

Kargol [ 15 ] proposed a set of modified KK equations that takes into account the effect of boundary layers on the passive transport across a membrane. The modified theory is shown to give better prediction for glucose flux across a nephrophane membrane. More recently, Li [ 16 ] derived a new set of KK equations for the transport of multiple ionic species across membranes.

## Bernoulli’s Effect – Relation between Pressure and Velocity

This work derived a new volume flux formulation which includes an additional driving force that originates from the transmembrane electrostatic potential difference. While these developments of the KK theory have covered a wide range of biophysical conditions, the effect of fixed charges has been neglected; KK theories to date have only considered mobile ions and employed the electroneutrality assumption i.

In the current study, we evaluate the influence of fixed charges on fluid and solutes transport across biological membranes. First we show that due to neglect of fixed charges, existing KK theories, including [ 1216 ], predict zero fluid pressure difference across membranes at thermodynamic equilibrium. We then employ linear nonequilibrium thermodynamics and propose a set of enhanced KK equations considering: The proposed theory is capable of recovering the Donnan equilibrium and predicting the correct fluid pressure that is required to balance the Donnan osmotic pressure at equilibrium state.

The analysis explains the swelling tendency of a charged electrolyte gel regardless of the presence of bounding layers. In addition to illustrating the fixed charge effect, we apply the proposed KK equations to study the water transport across active biological membranes, which was believed to be governed by the balance of osmotic pressure and fluid pressure [ 3 ]. Our analysis identifies an additional pressure mechanism that originates from active fluxes and from interactions between water and solutes in membrane transport processes.

This pressure force competes with the osmotic pressure on balancing the fluid pressure, and the new pressure balance condition implies that the values of the water potential on the two sides of separating membranes will not be equal in order to maintain the steady state of biological systems. To illustrate the importance of this new pressure mechanism, we apply the enhanced KK equations to quantify the transendothelial fluid pressure in the in vivo cornea, in which active transport mechanisms play crucial roles in regulating the fluid transport across the corneal endothelial layer.

**Bernoulli's Principle: High Velocity = Low Pressure**

The results show that the additional pressure mechanism has a significant impact on influencing the fluid pressure. Limitations of existing Kedem-Katchalsky theories In this section we describe a limitation of existing KK theories [ 1216 ] which are unable to recover the Donnan equilibrium when fixed charges exist on one side of the membrane.

## Hydraulic analogy

Consider a biological membrane that separates two polyelectrolyte solutions with fluid pressure P and P 0, solute concentrations C i and C. Basic circuit elements[ edit ] Conducting wire: Node in Kirchhoff's junction rule: A pipe tee filled with flowing water. A relatively wide pipe completely filled with water is equivalent to conducting wire.

When comparing to a piece of wire, the pipe should be thought of as having semi-permanent caps on the ends. Connecting one end of a wire to a circuit is equivalent to un-capping one end of the pipe and attaching it to another pipe.

With few exceptions such as a high-voltage power sourcea wire with only one end attached to a circuit will do nothing; the pipe remains capped on the free end, and thus adds nothing to the circuit. A resistor is equivalent to a constriction in the bore of the pipe which requires more pressure to pass the same amount of water. All pipes have some resistance to flow, just as all wires have some resistance to current.

A node or junction in Kirchhoff's junction rule is equivalent to a pipe tee. The net flow of water into a piping tee filled with water must equal the net flow out.

Voltage or current source: A dynamic pump with feedback control. A capacitor is equivalent to a tank with one connection at each end and a rubber sheet dividing the tank in two lengthwise [7] a hydraulic accumulator. When water is forced into one pipe, equal water is simultaneously forced out of the other pipe, yet no water can penetrate the rubber diaphragm. Energy is stored by the stretching of the rubber. As more current flows "through" the capacitor, the back-pressure voltage becomes greater, thus current "leads" voltage in a capacitor.

As the back-pressure from the stretched rubber approaches the applied pressure, the current becomes less and less. Thus capacitors "filter out" constant pressure differences and slowly varying, low-frequency pressure differences, while allowing rapid changes in pressure to pass through. An inductor is equivalent to a heavy paddle wheel placed in the current. The mass of the wheel and the size of the blades restrict the water's ability to rapidly change its rate of flow current through the wheel due to the effects of inertiabut, given time, a constant flowing stream will pass mostly unimpeded through the wheel, as it turns at the same speed as the water flow.

The mass and surface area of the wheel and its blades are analogous to inductance, and friction between its axle and the axle bearings corresponds to the resistance that accompanies any non-superconducting inductor. An alternative inductor model is simply a long pipe, perhaps coiled into a spiral for convenience. This fluid-inertia device is used in real life as an essential component of a hydraulic ram.

Various methods for measuring body water and extracellular volume have been extensively applied in clinical practice. However, precise determination of the optimal body fluid volumes encounters difficulties which are greatly accentuated in severe illnesses, because several other factors interacting with extracellular volume in determining tissue perfusion, including cardiac output, capacity of the blood vessels, and Starling forces, are significantly altered in these illnesses.

The aforementioned factors cause changes in the extracellular volume and create the need for optimal levels of this volume that are higher than those of healthy individuals and the need for newer methods for evaluating body fluid volumes.

### fluid dynamics - Relation between pressure, velocity and area - Physics Stack Exchange

Thus, fluid regulation in severe illness represents an evolving concept of body fluid balance separate from the two traditional concepts. Important questions about this third concept remain unanswered underscoring the need for further research. Its management is required in a variety of instances. These include stress that healthy individuals may experience at certain times, e. Proper fluid balance is a key management target for groups of individuals experiencing difficulties in maintaining normalcy with regard to it, e.

Less well known is the fact that disorders of fluid balance are encountered in conditions common in the general population, e. The diagnosis of fluid balance abnormalities requires the informed and reasoned interpretation of clinical and laboratory information[ 1419 ]. However, few would argue with the contention that the diagnostic accuracy of these methods is weak in general[ 1419 - 21 ] and is further complicated by the indiscriminate and inappropriate use of terms when expressing aspects of fluid balance.

The need to distinguish between pure water deficit and ECFV depletion has been stressed in the literature[ 24 - 26 ]. However, this approach has three limitations: This last difference justifies the introduction of a third approach to fluid balance, namely fluid balance in severe illness.

Our aim in this report is to review the methods of measuring TBW and ECFV, the uses and limitations of these methods, and the methods of evaluating fluid balance in patients with severe illness.

- Fluid balance concepts in medicine: Principles and practice

Osmolality, which expresses the total solute concentration in a fluid, is the core parameter of this concept[ 28 ]. The principal physiologic function that depends on this first fluid balance concept is the maintenance of stable volume of the body cells.

Stable body cell volume is critical for cell function and survival and is based on two membrane-related phenomena, active solute transport mechanisms of the cell membranes, mainly mediated by sodium-potassium ATPase, and high permeability of cell membranes to water[ 29 ].