WIND ENERGY SYSTEMS - Cd3wd

Chapter 7—Asynchronous Loads 7–47
compared with the high pressure alkaline cell.
7 PROBLEMS
1. You visit a farm where a wind turbine is driving a piston pump. You estimate the flow
rate to be 0.8 L/s, the stroke to be 0.18 m in length, and the operating speed to be 35
cycles per minute. Estimate the pump diameter. You will need to assume a reasonable
slip. Note: Systems installed in the United States prior to the mid 1980s were all sized
in English units, so any calculated value should be rounded to the nearest 0.5 inch to
express the size.
2. A rancher asks you for advice. His pumping head is 80 m and he needs 7000 liters of
water per day, with enough stock tank capacity to last for two calm days. What size
Dempster turbine and cylinder do you suggest?
3. Estimate the specific speed of the pump with characteristics shown in Fig. 7, assuming
the rated speed is 1750 r/min and the maximum diameter impeller is used.
4. A Jacuzzi Model 25S6M10XP-T submersible turbine pump has a maximum efficiency
of 70 percent at a capacity of 130 gal/min, a head of 550 ft, and a rotational speed of
3450 r/min.
(a) What is the specific speed?
(b) What is the required input power, both in horsepower and kW?
5. The pump in the previous problem is operated at 3000 r/min. Estimate the new head,
new capacity, and new input shaft power if the efficiency remains the same. Express in
English units.
6. You work for a company that is building a canal to carry water from the Missouri River
to Western Kansas for irrigation purposes. The water must be lifted a total of 300 m
in a series of stages of 10 to 20 m each. The total amount of water required per year
is 4 × 10 9 m 3 . This can be pumped intermittently throughout the year as the canal
supplies the necessary storage. You are asked to evaluate the concept of using wind
turbines with a 90 m blade diameter to drive the necessary pumps. The wind regime
can be characterized by the Weibull parameters k =2.2andc = 7.5 m/s. Cut-in, rated,
and furling wind speeds are assumed to be 0.6u m ,1.1u m ,and1.6u m , respectively, where
u me is given by Eq. 10. The peak pump efficiency is assumed to be 0.9 and the average
pump efficiency between cut-in and rated wind speeds is assumed to be 0.85.
(a) What is the total average power input to all the pumps on the canal?
(b) What is the total rated power input to all the pumps on the canal?
(c) How many wind turbines are needed?
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001