Chapter 6 Momentum and forces in fluid flow.ppt

Chapter 6
Momentum and Forces
in Fluid Flow
Momentum Equation
According to the law of momentum conservation ( Newton’s second law)
For a steady flow
1) Specially, for a steady flow with inlets and outlets
in which,
2) For one dimensional steady flow
Explaining
The equations above can be applied to only the inertial system or the coordinate system moving at uniform linear velocity because of being derived from Newton’s second law.
Example 6
In the following Fig.,the inflow and outflow radii are 25 and 15cm, respectively; the inflow and outflow angles with respect to the horizontal line (θ1andθ2) are 450 and 300, respectively; q is 50 L/s; the area average inlet and outlet pressure are and ; and the total fluid weight in the pipe is . Find the horizontal and vertical force required to hold the pipe in place.
Solution
The momentum exchange and force vectors are drawn in the following figure.
The magnitudes of Fp1 and Fp2 are calculated as
The magnitudes of v and qm are calculated as follows