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question3 describe equations 15 to 19 and connections between them...

Question: question3 describe equations 15 to 19 and connections between them...

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Question-3: Describe equations 1-5 to 1-9 and connections between them

Piping Systems Chap. 1 FIGURE 1-2 vane. U Flu1ป jet inpacting a moving , For example, in the case of conservation of linear momentum. the term à/àt JcvpVdVol is the time rate of accumulation of linear momentum within the con trol volume, and JispV V dA is the net efflux of linear momentum across the control surface. Since linear momentum is a vector quantity, Eq. (1-2) is basically a statement of Newtons law as applicable to a controi volume. This should serve to remind us that the reference frame for this expression must be inertial. This might seem like a subtle point, but it is extremely important if correct results are to be achieved. Consider the case of a fluid jet leaving a nozzle with absolute velocity V and im pacting a vane moving with absolute velocity U.A schematic representation is given in Fig. 1-2. The maximum power delivered to the wheeled vane occurs when U/V Now consider the same situation, except that the vane is part of an impulse turbine and the wheel speed U is rw. Equation (1-2) cannot be applied, since the reference frame is now a rotating frame and is not inertial. Equation (1-4) can be applied, with the re sult that the maximum power delivered now occurs when U/N -. Attempts to apply Eq. (1-2) to the turbine would lead to the incorrect result, UV This classical ex ample reminds us of the importance of choosing the appropriate conservation equation and reference frame. A streamline is a line that is tangent to the velocity vector of a flowing fluid. A path line is the loci of the spatial positions of a fluid particle as it traverses the flow field. If the flow is steady, the path line of a particle is also a streamline. Consider, as illus- trated in Fig, 1-3, a fluid element moving along a streamline in steady flow. If the addi- tional assumption of frictionless flow is made, then an application of Eq. (1-2) yields 2 (1-5) P &

1.9

where γ-ρ(g/g) is the specific weight and W, is the work per unit mass. Equation (1- R) is generally referred to as the energy equation and is the fundamental equation foran alyzing pipe flow. Information about losses must come from experimental data. The energy equation is normally written as 8 (1-9) Y 2R

Describe how equations 1-8 and 1-9 can help you design an energy system. What terms represent pump power and losses?

1.8

where the losses represent changes in internal energy Integration of Eq. (1-7) yields -2 + 2 /, + W, losses, (1-R)

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