Pumps in Series: Assuming that the pumps are identical, each pump must provide the following: Q (pump) = Qdes h(pump) = 0.5 hdes For example, if the design point for a given piping system were Qdes = 600 gpm, and hsys = 270 ft, the following pump selection criteria would apply: 1. Single pump system 2. Parallel pump system Q(pump) = 600 gpm, hp = 270 ft Q(pump) = 300 gpm, hp = 270 ft for each of the two pumps 3. Series pump system Q(pump) = 600 gpm, hp = 135 ft for each of the two pumps
Example 11.6 It is desired to use the 32 in. pump of Fig. 11.7a at 1170 rpm to pump water at 60˚C from one reservoir to another 120 ft higher through 1500 ft of 16 in. ID pipe with f = 0.030. Determine the operating point (hp & Q) and the pump power requirements and efficiency. Fig. E11.6 Head and system curves vs Q Neglecting minor losses, the energy equation can be written between the surfaces of the two reservoirs. Note that for these conditions the velocities at the reservoir surfaces is zero and kinetic energy change can be neglected.
V2 f L 0.030 ⋅1500 ft V 2 H s = z2 − z1 + = 120 ft + 2g D 1.333 ft 2 g Since from continuity we know that Q = V A = (π D /4) V, the energy equation becomes 2
H s = 120 ft + 0.269 Q H s = 120 ft + 1.335 Q
with Q in ft /s
Converting the flow rate Q to thousands of gal/min to be consistent with Fig. 11.7a we obtain 2
with Q in 10 gpm
Plotting the results for the system head and pump head vs. flow rate as shown in Fig. E11.6 we can graphically read a solution as H = 430 ft and Q = 15,000 gpm
From Fig. 11.7a, the pump power and efficiency at the operating point are BHP ≅ 2000 hp and h ≅ 80%
It is noted that a more common piping / pump system design and selection problem would proceed as follows: (1) The basic geometry, components and specifications of a piping system would be specified including a known design flow rate, Qdes. (2) Solve the energy equation for hsys for a range of flow rates including Qdes. (3) Plot the system head curve vs flow rate and identify the design head requirements hdes at Qdes. (4) Review pump curves from various manufacturers to identify several pumps or pump systems capable of providing hp ≅ hdes at Qdes. (5) Select final choice for pump or pump system to meet design based on additional factors such as (a) closeness of hp to hdes, (b) pump efficiency and power requirements at design point, (c) pump costs. Wind Turbines Wind energy has been used to supply mechanical power for irrigation and electrical power for many years. Modern technology has led to the development of wind turbine systems that are beginning to see extensive use to supply electrical power for the power grid system in many countries. A simple streamtube model as shown in Fig. 11.30 will be used to develop a basic analysis for wind turbine performance.
Fig. 11.30 Streamtube model for flow through a wind turbine
Consider the control volume shown in Fig. 11.30, the momentum equation can be written between points 1 and 2 as
! ∑ Fx = − F = m (V2 − V1 )
Likewise, considering the control volume just before and after the disk, the momentum equation can be written as
! ∑ Fx = − F + (Pb − Pa ) A = m (Va − Vb )
Equating these equations, we obtain for the propeller force
! F = (Pb − Pa ) A = m (V1 − V2 )
The incompressible Bernoulli equation can be written before and...