# Relationship between speed of water and pressure gradient

### Pressure-gradient force - Wikipedia

What is the relationship between pressure differential and the amount of fluid that layers of water and has low pressure and has high velocity at the exit of pipe. The water volume inside the balloon did not change, but the pressure in the This pressure gradient is analogous to the difference in pressure between two. So if you quadruple the pressure difference, you get twice the speed. . You can obtain relation between water column height and pressure in container so basically velocity is proportional to the square root of differential.

One way is to tilt the pipe so the flow is downhill, in which case gravitational kinetic energy is transformed to kinetic energy. The second way is to make the pressure at one end of the pipe larger than the pressure at the other end. A pressure difference is like a net force, producing acceleration of the fluid.

As long as the fluid flow is steady, and the fluid is non-viscous and incompressible, the flow can be looked at from an energy perspective.

### fluid dynamics - Relation between water flow and pressure - Physics Stack Exchange

This is what Bernoulli's equation does, relating the pressure, velocity, and height of a fluid at one point to the same parameters at a second point. The equation is very useful, and can be used to explain such things as how airplanes fly, and how baseballs curve.

Bernoulli's equation The pressure, speed, and height y at two points in a steady-flowing, non-viscous, incompressible fluid are related by the equation: Some of these terms probably look familiar If the equation was multiplied through by the volume, the density could be replaced by mass, and the pressure could be replaced by force x distance, which is work.

Looked at in that way, the equation makes sense: For our first look at the equation, consider a fluid flowing through a horizontal pipe. The pipe is narrower at one spot than along the rest of the pipe. By applying the continuity equation, the velocity of the fluid is greater in the narrow section.

Is the pressure higher or lower in the narrow section, where the velocity increases? Your first inclination might be to say that where the velocity is greatest, the pressure is greatest, because if you stuck your hand in the flow where it's going fastest you'd feel a big force. The force does not come from the pressure there, however; it comes from your hand taking momentum away from the fluid.

The pipe is horizontal, so both points are at the same height. Bernoulli's equation can be simplified in this case to: The kinetic energy term on the right is larger than the kinetic energy term on the left, so for the equation to balance the pressure on the right must be smaller than the pressure on the left. It is this pressure difference, in fact, that causes the fluid to flow faster at the place where the pipe narrows.

Steeper gradients result in a stronger push. Identification Surface weather maps depict barometric pressure with lines of equal pressure or isobars. These lines, also known as pressure contours, are normally in intervals of four millibars mb.

These contours form circles around high and low pressure systems on a map. Tightly spaced contours mean high winds. Because pressure generally decreases with height, a smoothing method is used that converts all stations to standard sea level pressure which is considered to be mb or Mathematics of gradient The high to low force that causes wind and its velocity works on synoptic scales such as those depicted on conventional surface maps.

Resistance R is a term most of us understand from everyday life.

We speak of people being resistant to change or taking the path of least resistance. This concept translates well to the cardiovascular system because blood flow also takes the path of least resistance. An increase in the resistance of a blood vessel results in a decrease in the flow through that vessel.

What parameters determine resistance? For fluid flowing through a tube, resistance is influenced b by three components: The following equation, derived by the French physician Jean Leonard Marie Poiseuille and known as Poiseuille's law shows the relationship of these factors: To remember these relationships, think of drinking through a straw. You do not need to suck as hard on a short straw as on a long one the resistance offered by the straw increases with length.

Drinking water through a straw is easer than drinking a thick milkshake resistance increases with viscosity. And drinking the milkshake through a big fat straw is much easier than through a skinny cocktail straw resistance increases as radius decreases.

How significant are tube length, fluid viscosity, and tube radius to blood flow in a normal individual? The length of the systemic circulation is determined by the anatomy of the system and is essentially constant. Blood viscosity is determined by the ratio of red blood cells to plasma and by how much protein is in the plasma.

Normally, viscosity is constant, and small changes in either length or viscosity have little effect on resistance.

### The Relationship Between Pressure Gradient & Wind Speed | Sciencing

This leaves change in the radius of the blood vessels as the main variable that affects resistance in the systemic circulation.

Let's return to the example of the straw and the milkshake to illustrate how changes in radius affect resistance. If we assume that the length of the straw and the viscosity of the milkshake do not change, this system is similar to the cardiovascular system - the radius of the tube has the greatest effect on resistance. Because flow is inversely proportional to resistance, flow increases fold when the radius doubles.

As you can see from this example, a small change in the radius of a tube has a large effect on the flow of a fluid through that tube.

Thus a small change in the radius of a blood vessel will have a large effect on the resistance to blood flow offered by that vessel. A decrease in blood vessel diameter is known as vasoconstriction [vas, a vessel or duct]. An increase in blood vessel diameter is called vasodilation. Vasoconstriction decreases blood flow through a vessel; vasodilation increases blood flow through a vessel. If the pressure gradient remains constant, then flow will vary inversely with resistance.

Velocity of Flow Depends on the Flow Rate and the Cross-Sectional Area The word flow is sometimes used imprecisely in cardiovascular physiology, leading to confusion.

## Pressure-gradient force

Flow usually means flow rate, the volume of blood that passes a given point in the system per unit time. Flow rate should not be confused with velocity of flow, the distance a fixed volume of blood travels in a given period of time.

Velocity of flow is a measure of how fast blood flows past a point. Flow rate measures how much volume of blood flows past a given point in a given period of time. For example, look through the open door at the hallway outside your classroom. The number of people passing the door in one minute is the flow rate of people through the hallway.

How quickly those people are walking past the door is their velocity of flow. In a tube of fixed diameter and thus fixed cross-sectional areavelocity of flow directly related to flow rate.