Bernoulli's example problem (video) | Fluids | Khan Academy
Pressure drop in pipes is caused by: Friction, Vertical pipe difference or To determine the fluid (liquid or gas) pressure drop along a pipe or pipe component, the following calculations, in the following order. ρ = Density of fluid (kg/m3). Pressure Drop - Air Flow Relationship for Soybeans o o 81 . flow encountered in the conveying of this material of high density did 2 goD h m -, >, Learn more about pressure, buoyant force, and flowing fluid so you can appreciate the AP® Calculus BC · AP® Statistics · Multivariable calculus · Differential equations · Linear algebra Density and Pressure . And now, a direct relationship to God, unmediated by the institution of the Catholic Church, was possible.
Friction Factor The Moody diagram in Figure 1 is a classical representation of the fluid behavior of Newtonian fluids and is used throughout industry to predict fluid flow losses. It graphically represents the various factors used to determine the friction factor. For example, for fluids with a Reynolds number of and less, the flow behavior is considered a stable laminar fluid and the friction factor is only dependent on the Reynolds number .
Fluids with a Reynolds number between and are considered unstable and can exhibit either laminar or turbulent behavior. This region is commonly referred to as the critical zone and the friction factor can be difficult to accurately predict.
Judgment should be used if accurate predictions of fluid loss are required in this region. Either Equation 1 or 3 are commonly used in the critical zone. If the Reynolds number is beyondthe fluid is considered turbulent and the friction factor is dependent on the Reynolds number and relative roughness. For Reynolds numbers beyondthe Moody diagram identifies two regions, transition zone and completely turbulent zone.
The friction factor represented in these regions is given by the Colebrook formula which is used throughout industry and accurately represents the transition and turbulent flow regions of the Moody diagram.
The Colebrook formula for Reynolds number over is given in equation 3. The roughness factor is defined as the absolute roughness divided by the pipe diameter or. Typical values of absolute roughness are 5.Fluids in Motion: Crash Course Physics #15
The Colebrook equation has two terms. The second term,is dominate for fluid flow where the relative roughness lines converge smooth pipes. Liquid Incompressible Flow For liquid flow, equation 4 has been used by engineers for over years to calculate the pressure drop in pipe due to friction.
This equation relates the various parameters that contribute to the friction loss. This equation is the modified form of the Darcy-Weisbach formula which was derived by dimensional analysis. The friction factor in this equation is calculated by equation 3 for a specified Reynolds number and roughness factor using an iterative method or a trial and error procedure.
Bernoulli's example problem
Gas Compressible Flow For gas flow, density is a strong function of pressure and temperature, and the gas density may vary considerably along the pipeline. Due to the variation of density, equation 5 should be used for calculation of friction pressure drop. Again, the friction factor in this equation is calculated by equation 3 for a specified Reynolds number and roughness factor using a trial and error procedure.
Actual volume flow rate is needed to calculate the velocity of gas in the line from which the Reynolds number is calculated. Equation 6 may be used to convert the volume flow rate at standard condition to the actual volume flow rate. Surface Tension and Adhesion Video transcript Let's say I have a horizontal pipe that at the left end of the pipe, the cross-sectional area, area 1, which is equal to 2 meters squared.
Let's say it tapers off so that the cross-sectional area at this end of the pipe, area 2, is equal to half a square meter.
We have some velocity at this point in the pipe, which is v1, and the velocity exiting the pipe is v2. The external pressure at this point is essentially being applied rightwards into the pipe. Let's say that pressure 1 is 10, pascals. The pressure at this end, the pressure that's the external pressure at that point in the pipe-- that is equal to 6, pascals.
Given this information, let's say we have water in this pipe. We're assuming that it's laminar flow, so there's no friction within the pipe, and there's no turbulence.
Using that, what I want to do is, I want to figure out what is the flow or the flux of the water in this pipe-- how much volume goes either into the pipe per second, or out of the pipe per second? We know that those are the going to be the same numbers, because of the equation of continuity.
We know that the flow, which is R, which is volume per amount of time, is the same thing as the input velocity times the input area. This immediately tells us that v2 is coming out at a faster rate, and this is based on the size of the openings.
Fluids | Physics | Science | Khan Academy
We know, because V2 is coming out at a faster rate, but we also know because we have much higher pressure at this end than at this end, that the water is flowing to the right. The pressure differential, the pressure gradient, is going to the right, so the water is going to spurt out of this end.
And it's coming in this end. Let's use Bernoulli's equation to figure out what the flow through this pipe is. Let's just write it down: This pipe is level, and the height at either end is the same, so h1 is going to be equal to h2.