1,A hydroelectric plant utilizing a continuous flow of 15CFS with an absolute he

Question

1,A hydroelectric plant utilizing a continuous flow of 15CFS with an absolute head of 900ft was buit 4 ears ago. The 20" diameter existing pipeline cost $200,000 for pipe, installation and right of way has a friction head loss of 85ft. Additional water rights have been acquired which will result in a total flow of 30CFS. The following plans are under consideration for using the total available water flow. Plan I use the present pipeline. This will entail no additional expense but will increase the friction head by a factor of 4 to 340 ft. Plan II, add an additional 20" pipeline at a cost of $100,000. The loss of head for this pipeline will now be 85ft, as each pipeline carries 15CFS as before. Plan III is to build a 26" diameter pipeline at a cost of $200,000 and remove the existing line for which a $10,000 can be realized as scrap. The energy of the water delivered to the turbine of the power plant is valued at $135 per horsepower year. Horsepower is given by HP= h x F x 62.4/550, where his head in feet (900-friction loss) and F is the flow in CFS. Insurance and taxes are 5% of first cost for all three plans. Operating and maintenance costs are the same for all three plans. Marr is 12%. If all lines are retired in 25 years without any salvage value, what are the comparable annual costs for the three plans?

Explanation / Answer

The existing pipeline has dia, d =20 ‘’ with absolute head of 900’ and friction loss of 85’. The pipe carries total discharge of 15 CFS, with total cost of installation for pipe is $ 200,000.

Now, since total water quantity available has been increased to 30 CFS, to accommodate this increase of 15 CFS, 3 plans are proposed and their total annual cost has to be compared to arrive at most economical solution.

Point to Note:

PLAN 1: To use the present pipeline

Advantages: 1. No additional expenses on installation of new pipeline

Demerit: 1. Increase in friction head from 85’ to 340’ by a factor of 4.

Since, there is no new pipeline being installed, no additional expense incurred. But, @ 5% for both maintenance and repair and insurance and taxes has to be paid annually for initial cost of $ 200,000.

I.e. $ 20,000 on taxes and maintenance.

As a result of increase in friction head, net head is reduced to 560’ which generated for 30 CFS water, 1906.04 horsepower. So, in a single year revenue from power generated = 135* 1906.04 = $ 257, 314

But, profit is revenue – expenses, i.e. $ 257,314 - $ 20,000 = $ 237, 314

Calculations shown in the table below

Plan 2: Install a new pipeline of dia 20’’

Advantages: 1. Friction head remains same for both the new and old pipeline at 85’ and both carries discharge of 15 CFS.

Demerits: 1. Installation cost of $ 100,000 for the new pipeline.

Since, an extra 20’’ pipeline is to be installed for $ 100,000. Both maintenance and repair & insurance and taxes @ 5% has to be paid annually for initial cost of $ 200,000 + $ 100,000 = $ 300,000

I.e. $ 30,000 on taxes and maintenance.

For both the pipeline, net head is reduced to 815’ which generated for 15 CFS water each, 1386.98 horsepower. So, in a single year revenue from power generated = 135* 2*1386.98 = $ 374, 485

But, profit is revenue – expenses, i.e. $ 374,485 - $ 130,000 = $ 244, 485

Calculations shown in the table below

Plan 3: Install a new pipeline of dia 26’’ and remove the existing 20’’ dia pipeline

Advantages: 1. $ 10,000 can be realized as scrap for the removed old pipeline

Demerits: 1. Installation cost of $ 200,000 for the new pipeline.

Since, 26’’ pipeline is to be installed for $ 200,000 and old pipeline has scrap value of $ 10,000. Both maintenance and repair & insurance and taxes @ 5% has to be paid annually for initial cost of $ 200,000

I.e. $ 20,000 on taxes and maintenance.

For the pipeline, net head is reduced to 815’ which generated for 30 CFS water, 2773.96 horsepower. So, in a single year revenue from power generated = 135*2773.96 = $ 374, 485 and an additional $ 10,000 from Scrap

Total revenue = $ 384,485

But, profit is revenue – expenses, i.e. $ 384,485 - $ 220,000 = $ 164, 485

Calculations shown in the table below

So, Plan 2 is the most appropriate plan of all 3 to maximize the profit and ensure maximum utilization

Expenses Absolute head Friction head Net head (h) Flow (F) Horsepower generated Revenue Generated Additional Revenue Total Revenue Profit Initial cost Operation & Maintenance Insurance and Taxes Total (ft) (ft) (ft) (CFS) (h*F* 62.4/550) @ 135/ horsepower year Revenue - Expense 0 10,000 10,000 20,000 900 340 560 30 1906.04 257314.91 0 257314.91 237,314.91

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