A storage reservoir supplies water to a pressure turbine under a head of 20 m. If the flow rate is 500 liters per second the head loss in the 300 mm pipe supplying the turbine is 2.5 m. Determine the pressure at the entrance of the turbine. If a negative pressure of 30 kPa exists at the 600 mm diameter section of the draft tube (exit tube) below the turbine 1.5 m below the supply line, estimate the energy absorbed by the turbine in kW neglecting losses between the entrance and exit of the pipe. Find also the output of the turbine assuming an efficiency of 85%

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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A storage reservoir supplies water to a pressure
turbine under a head of 20 m. If the flow rate is 500
liters per second the head loss in the 300 mm pipe
supplying the turbine is 2.5 m. Determine the
pressure at the entrance of the turbine. If a negative
pressure of 30 kPa exists at the 600 mm diameter
section of the draft tube (exit tube) below the turbine
1.5 m below the supply line, estimate the energy
absorbed by the turbine in kW neglecting losses
between the entrance and exit of the pipe. Find also
the output of the turbine assuming an efficiency of
85%
Transcribed Image Text:A storage reservoir supplies water to a pressure turbine under a head of 20 m. If the flow rate is 500 liters per second the head loss in the 300 mm pipe supplying the turbine is 2.5 m. Determine the pressure at the entrance of the turbine. If a negative pressure of 30 kPa exists at the 600 mm diameter section of the draft tube (exit tube) below the turbine 1.5 m below the supply line, estimate the energy absorbed by the turbine in kW neglecting losses between the entrance and exit of the pipe. Find also the output of the turbine assuming an efficiency of 85%
Sample problems:
1. A liquid (sp gr 2.0) is flowing in a 50 mm diameter pipe. The total energy at a given
point is found to be 75 J/kg. The elevation of the pipe above the datum line is 3 m,
and the pressure in the pipe is 65.5 kPa. Compute the velocity of flow and the
horsepower in the stream at that point.
Given:
EGL = energy gradient line
V2
2g
HGL hydraulic gradient line
E
50 mm ø pipe
Q
• point
Datum line
E = 75 J/kg = 75 N.m/kg (1kg/9.81N) = 7.645 m
Z = 3 m
p = 65.5 KPa = 65.5 KN/m²
D = 50 mm = 0.050 m
Sp. Gr. = 2.0
w = 2 (9810) = 19620 N/m3 = 19.62 KN/m³
%3D
Required:
V and WHP
Solution:
V2
+
E =
2g
+ Z
V2
65.5
+
19.62
7.645 =
+3
2g
V2
= 7.645 – 6.338
2g
V = V(2g)(1.307) = 5.064m/s
wQH
WHP =
746
WAVE
19620 (4) D?(5.064)(7.645)
WHP =
746
746
2
50
19620 (4) To00) (5.064)(7.645)
1000.
WHP =
1.999hp
%D
746
Transcribed Image Text:Sample problems: 1. A liquid (sp gr 2.0) is flowing in a 50 mm diameter pipe. The total energy at a given point is found to be 75 J/kg. The elevation of the pipe above the datum line is 3 m, and the pressure in the pipe is 65.5 kPa. Compute the velocity of flow and the horsepower in the stream at that point. Given: EGL = energy gradient line V2 2g HGL hydraulic gradient line E 50 mm ø pipe Q • point Datum line E = 75 J/kg = 75 N.m/kg (1kg/9.81N) = 7.645 m Z = 3 m p = 65.5 KPa = 65.5 KN/m² D = 50 mm = 0.050 m Sp. Gr. = 2.0 w = 2 (9810) = 19620 N/m3 = 19.62 KN/m³ %3D Required: V and WHP Solution: V2 + E = 2g + Z V2 65.5 + 19.62 7.645 = +3 2g V2 = 7.645 – 6.338 2g V = V(2g)(1.307) = 5.064m/s wQH WHP = 746 WAVE 19620 (4) D?(5.064)(7.645) WHP = 746 746 2 50 19620 (4) To00) (5.064)(7.645) 1000. WHP = 1.999hp %D 746
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