Holooly Plus Logo
Holooly Plus Logo

Question 16.SP.8: A small Francis runner with a diameter of 2.0 ft is tested a......

A small Francis runner with a diameter of 2.0 ft is tested and found to have an efficiency of 0.893 when operating under most efficient conditions. Approximately what would be the efficiency of a homologous runner having a diameter of 6.0ft ?

Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

Eq. (16.15): 1−ηm1−ηp=(DpDm)1/5=(62)1/5=30.2=1.246\quad \frac{1-\eta_{m}}{1-\eta_{p}}=\left(\frac{D_{p}}{D_{m}}\right)^{1 / 5}=\left(\frac{6}{2}\right)^{1 / 5}=3^{0.2}=1.246

1−ηp=(1−0.893)/1.2461-\eta_{p}=(1-0.893) / 1.246

From which:        ηp=0.914=91.4%\eta_{p}=0.914=91.4 \%

1−ηm1−ηp≈(DpDm)1/5 \frac{1-\eta_m}{1-\eta_p} \approx\left(\frac{D_p}{D_m}\right)^{1 / 5}         (16.15)

Related Answered Questions

Question: 16.SP.13

Repeat Sample Prob. 16.12, assuming the Francis turbine is at sea level with a water temperature of 80°F. Check the result against Fig. 16.16 ...

Verified Answer:

Table A.3 at sea level: \quad \frac{p_{\tex...
Question: 16.SP.14

Two or more identical turbines are to be selected for an installation where the net head is 350 ft and the total flow is to be 600 cfs. Select turbines for this installation assuming  90 % efficiency for all turbines. ...

Verified Answer:

The total available power is \frac{\gamma ...
Question: 16.SP.12

Find the maximum permissible head under which a Francis turbine (Ns=70) can operate if it is set 10 ft above tailwater at an elevation of 5000ft with water temperature at 60°F. ...

Verified Answer:

Table A.3 at 5000ft5000 \mathrm{ft} eleva...
Question: 16.SP.11

Assume the Francis turbine of Sample Prob. 16.6 is operating at maximum efficiency. Find the specific speed of the turbine and estimate the diameter of its runner. ...

Verified Answer:

Eq. (16.21):             \quad N_{s}=\left(...
Question: 16.SP.10

A turbine homologous to the turbine of Sample Prob. 16.9 has all dimensions one-half as large. For this turbine find the speed of rotation, flow rate, and brake horsepower when operating under the same net head of 81ft. ...

Verified Answer:

Eq. (16.16): If hh does not change, ...
Question: 16.SP.9

A given turbine runs at a maximum efficiency of 87% when discharging 200 cfs at 150 rpm under a net head of 81 ft. This turbine drives an electric generator that is developing 60-cycle current. ( a ) How many poles are required for this generator? (b) What would be the speed, flow rate, and brake ...

Verified Answer:

(a)                 N=\frac{7200}{n}=\frac{...
Question: 16.SP.7

Refer to Fig. 16.11. A draft tube leading from the discharge side of the turbine to the submerged discharge into the tailrace consists of a 40 -ft-long pipe (f=0.03) of constant diameter 3ft. The flow rate is 130 cfs. If this draft tube were replaced by a diverging tube of length 40ft whose diameter ...

Verified Answer:

Original draft tube: Head loss due to draft tube, ...
Question: 16.SP.6

Francis turbine operating at 300 rpm develops a shaft horsepower of 1125 hp when the flow is 120cfs. Find the torque transmitted from the flowing water to the shaft. ...

Verified Answer:

Shaft power =Tω=T \omega \begin...
Question: 16.SP.4

Refer to Fig. 16.1. Water is delivered from a reservoir through a 4-ft-diameter pipe (f=0.025)10,000ft long to a nozzle that emits an 8-in-diameter jet that impinges on an impulse wheel. The surface of the reservoir is at an elevation 2420 ft higher than the nozzle. The impulse wheel is connected ...

Verified Answer:

Energy equation from surface of reservoir to jet n...
Question: 16.SP.3

Demonstrate that when taking account of fluid friction in the buckets of an impulse wheel by using kv²2/2g with values of k ranging from 0.2 to 0.6, this is nearly equivalent to v2=0.8−0.9 times v1. ...

Verified Answer:

\frac{v_1^2}{2 g}-h_L=\frac{v_2^2}{2 g}, \q...