unsteady stateThe unsteady state mass conservation equation for chlorine concentration decay in drinking water in a pipe for axisymmetric flow is solved by using Hankel transform for low peclet number. The solution is obtained analytically for the model and the numerical values and their graphical ...
For example, remaining in the domain of transport phenomena, here are some of the ceteris paribus conditions involved in deriving the Hagen-Poiseuille equation (for flow in a cylindrical pipe) from the Navier-Stokes equations. The flow is laminar (i.e. the Reynolds number is less than about ...
In a sense, the mass flow rate is the measure of the amount of fluid flowing through, say, a pipe, while the volumetric flow rate is the measure of 3D space occupied by the fluid that's passing through a pipe.Volume Flow Rate Equation Mass Flow Rate to Velocity Continuity Equation ...
Fluid Flow & Continuity Equation Practice Problems 31 problems 1PRACTICE PROBLEM Reducers are devices that connect pipes of different cross-sections. A pipeline has a reducer that connects a 3.0 inch diameter pipe to a 2.0 inch diameter pipe. If water in the large pipe flows at 10 cm/s, how...
They proposed that constant b, by analogy with pipe flow, should be dependent on surface roughness. They also found that the voidage dependence in Eq. (2) is not accurate over a wide range of voidages, and with ε3.6 instead of ε3 it would result in a better fit. In the modified ...
Can the equation be used for gases?Yes, it can be used for gases, but factors like compressibility become more significant and should be considered. Is the flow rate always constant in a pipe?The flow rate can be constant if the pipe has a constant cross-section and a steady, incompressib...
For example, if v2 is greater than v1 in the equation, then P2 must be less than P1 for the equality to hold. Example 1. Calculating Pressure: Pressure Drops as a Fluid Speeds Up In Example 1 from Flow Rate and Its Relation to Velocity, we found that the speed of water in a hose...
The Reynolds Number is the ratio of the inertial and viscous forces of a fluid's flow: $$Re = \frac{inertial force}{viscous force} $$ The expressions for the two terms simplify into a ratio that provides the Reynolds number formula: $$Re = \frac{\rho vd}{\mu} $$ with each of ...
4.8 Availability Balance for an Open System The availability balance of a closed system was derived in Section 4.7. A similar approach can be used to evaluate the change of availability in an open system. The Unsteady Flow Energy Equation (see Chapter 1, Eqn (1.30)) is (4.44)∑jQ˙−W...
Using conservation equations and boundary conditions for cylindrical coordinates, the laminar flow has a parabolic profile from zero at the wall to a maximum velocity at the centerline (Fig. 1.25), Sign in to download full-size image Figure 1.25. Longitudinal cutting view of a pipe with a ...