# Relation Between Flow And Pressure Pdf

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- Relationship Between Pressure Drop and Flow Rate in a Pipeline
- Pipe Pressure Drop Calculations
- Pressure-based Flowmeters

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## Relationship Between Pressure Drop and Flow Rate in a Pipeline

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Rate of FlowIntroduction:Pressure is the exertion of force upon a unit area by a surface of an object in a perpendiculardirection. When fluid flows through pipe, there are two main forces acting on it. One is the frictional forcethat is made by the side of the pipe, and the other one is the viscous force in the fluid. Near thewall of the pipe, there is a thin layer of fluid that sticks to the pipe.

In the middle of the pipe, thewater moves faster and consistently. The viscous force of fluid makes a shearing action whichwill result in a small layer of fluid that will keep on increasing until it reach the speed of the freeflowing in the center of the pipe.

The energy is lost from these two forces. Ideal fluid has a steady flow, nonviscous flow, irrational flow, and incompressible flow. Steadyflow is when the particles flow after each other in a stream line and all particles has the samevelocity.

Nonviscous flow is when there are no shearing forces in the fluid and will result inproducing heat as the fluid flows. Irrational flow is when there will be no turmoil in the form ofeddy currents or whirlpools. Incompressible flow is when the density of the fluid is constant. Fluid pressure is defined as the pressure at some point within a fluid.

This occurs in two differentconditions, one is an open condition open channel flow and the other one is a closed condition conduits. In an open condition, the pressure stays the same which follow the principle of fluidstatics.

In a closed condition can be static when the fluid does not move and it can be dynamicwhen the fluid can move in a pipe. This follows the principle of fluid dynamics. The fluidpressure is a characteristic of the discoveries of Daniel Bernoulli.

As the kinetic energy of thewater decreases, the pressure increases. When a cross sectional area of a pipe decreases, thekinetic energy of water increases leading to a decrease in pressure. This is called the BernoulliEffect.

The equation for the flow rate of water coming out of the hole is shown below: [2]Where v is the velocity of the water, Q is the flow rate of the water, and A is the cross sectionalarea of the hole.

Design:Research Question:How does the water pressure inside a cylindrical container affect its water flow rate? Variables:The independent variable is the water pressure inside the cylindrical container which iscontrolled by the height of water in the container. The dependent variable is the water flow rate. The controlled variables in this experiment was the amount of time per trials 10 seconds whichcan be measured using a stopwatch, the temperature of water using the same source of water, theheight where the experiment was done constant acceleration or gravity , the cylindricalcontainer, and the density of water using the same source of water.

Materials and Procedure:Cut a small 5. Use modeling clay to close the hole. Fill the water into the container only up to the most toppart of the largest diameter. Make sure that the water does not leak out or push the clay out. Stick themeter stick into the middle of the container and measure the height of the water in the container. Start thestopwatch and pull the clay out at the same time.

When the stopwatch reaches 10 seconds, close the hole on the watercontainer with the clay. Measure the height of the water in the container again and measure the height ofwater in the ml graduated cylinder. Empty out the water in the graduated cylinder. Repeat theseitalicize steps for the next five trials with different height of water in the container ranging from 7 to 33centimeters. Note that the diameter of the hole is 5. The bottom of the container to the hole is 7 cm.

Notethat the calculated average height of water is found by subtracting the average height by 4 since there is asmall concave bump at the bottom of the container. Figure 2: Shows the quadratic relationship between the pressure and flow rate.

Figure 3: Shows the proportional relationship between the pressure and the flow rate squared. Figure 4: Shows the high-low fit for the pressure and flow rate squared graph according to figure 3. Therange of the two slopes is 0. The range of the two y-intercepts is withan uncertainty of 6. Sample Calculations:Finding the attuned average heightFinding the calculated average pressure difference:Finding the Uncertainty for the calculated average pressure difference:Finding the Uncertainty for the change in volume: 7.

Finding the average flow rate of the water:Finding the uncertainty for the average flow rate of the water:Finding uncertainty of the average flow rate squared:Conclusion:The relationship of the equation between the pressure and the water flow rate squared accordingto figure 3 and figure 4 is shown below: [4]The equation 3 states that the relationship between the pressure and the water flow rate squaredshould be proportional to each other. The results clearly support this relationship. This showsthat the results in this experiment are highly confident because the line of best fit in figure 3 goesthrough all the data point in their uncertainties.

The slope of equation 4 is a constant and will remain constant even though the water flowrate squared changes. This is because the density of water and the area of the hole areconstant.

The y-intercept should be zero because if the pressure difference is zero, then the waterflow rate squared should be zero too due to the fact that the water does not flow out the containerresulting in a directly proportional relationship. The limitation of this experiment only applies to water flowing out of a standard 5 gallon watercontainer with a small opening hole with a height of water ranging from 7 to 33 centimeters.

Evaluation:A systematic error in this experiment is the kinetic energy of the water in the water container isassumed to be zero. As the water flows out of the container, the water in the container woulddecrease therefore the kinetic energy of the water cannot be zero. This could be improved byusing a high speed video camera to calculate the velocity of the water and the level of the water.

A human error in this experiment is the time taken to close the hole. It is very hard to close thehole in an exact 10 seconds. There might be problems when closing the hole with modeling clay. This error could be improved by using a smaller hole and a larger time frame. Another error might be finding the pressure using the average height of the water. This is anaccurate way of measuring the pressure because if the height is measured in a more accurateway, then the height must be measured every one second instead of ten seconds.

This error couldbe fixed by using a high speed video camera to measure the heights of water during each trialsand use this value to calculate the average height for ten seconds. You just clipped your first slide! Clipping is a handy way to collect important slides you want to go back to later.

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## Pipe Pressure Drop Calculations

Designing Air Flow Systems. A theoretical and practical guide to the basics of designing air flow systems. Download Word document. Air Flow. Types of Flow.

The power required to overcome friction is related to the pressure drop through. Power. P Q. = ∆ or we can substantial compared to those for flow through short straight pipe segments. Losses are can use the empirical relation. 2. 2. 1.

## Pressure-based Flowmeters

New User? All Sensors Pressure Points are application tips to simplify designing with microelectromechanical systems MEMS pressure sensors and avoiding common pitfalls. Fluid flow occurs with the motion of liquid and gaseous materials and pressure sensors play a critical role in determining many aspects of fluid flow. Fluid dynamics provides the means of understanding the parameters that impact fluid flow. The active links in the following sections provide more details.

Contact Today. Instruments should be ranged to measure not only expected values but all values the system can produce. During upsets, actual values often exceed 20mA values for instruments tightly ranged for normal process conditions. But nonlinear relationships complicate scale adjustments.

#### Calculating the Pressure Drop in a Pipe

To calculate the pressure loss in a pipe it is necessary to compute a pressure drop, usually in fluid head, for each of the items that cause a change in pressure. However to calculate the friction loss in a pipe for example, it is necessary to calculate the friction factor to use in the Darcy-Weisbach equation which determines the overall friction loss. The friction factor itself is dependent on internal pipe diameter, the internal pipe roughness and the Reynold's number which is in turn calculated from the fluid viscosity, fluid density, fluid velocity and the internal pipe diameter. There are therefore a number of sub-calculations that must take place to calculate the overall friction loss. Working backwards we must know the fluid density and viscosity properties, know the pipe diameter and roughness properties, calculate the Reynold's number, use this to calculate the friction factor using the Colebrook-White equation, and finally plug in the friction factor to the Darcy-Weisbach equation to calculate the friction loss in the pipe. After calculating the pipe friction loss we then need to consider possible fitting losses, change in elevation and any pump head added. The following sections consider each calculation in turn.

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