Fluid mechanics and hydraulics miscellaneous
- A pipe of 0.7 m diameter has a length of 6 km and connects two reservoirs A and B. The water level in reservoir A is at an elevation 30 m above the water level in reservoir B. Halfway along the pipe line, there is a branch through which water can be supplied to a third reservoir C. The friction factor of the pipe is 0.024. The quantity of water discharged into reservoir C is 0.15 m³/s. Considering the acceleration due to gravity as 9.81 m/s² and neglecting minor losses, the discharge (in m³ /s) into the reservoir B is ______________
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0.5716
Friction loss hƒ = ƒLv² 2gD
Q = AV∴ V = Q A A = π D² 4 
= 16ƒLQ² 2gπD5 
Let discharge of reservior A = Q.
Consider lengths 1 and 2.
hƒ1 + hƒ2 = 30 m= 16ƒL × (Q)² + 16ƒL × (Q - 0.15)² = 30 2gπ × (7)5 2gπ × (7)5 ⇒ 16 × 0.15 × 3000 [Q² + (Q - 0.15)²] = 30 2 × 9.81 × π × (0.7)5
⇒ Q = 0.7216 m³/s
⇒ QB = Q – 0.15 = 0.5716 m³/sCorrect Option: D
0.5716
Friction loss hƒ = ƒLv² 2gD
Q = AV∴ V = Q A A = π D² 4 = 16ƒLQ² 2gπD5
Let discharge of reservior A = Q.
Consider lengths 1 and 2.
hƒ1 + hƒ2 = 30 m= 16ƒL × (Q)² + 16ƒL × (Q - 0.15)² = 30 2gπ × (7)5 2gπ × (7)5 ⇒ 16 × 0.15 × 3000 [Q² + (Q - 0.15)²] = 30 2 × 9.81 × π × (0.7)5
⇒ Q = 0.7216 m³/s
⇒ QB = Q – 0.15 = 0.5716 m³/s
- A hydraulic jump is a 2m wide rectangular channel which is horizontal and frictionless. The post-jump depth and velocity are 0.8 m and 1m/s, respectively. The pre-jump velocity is ___________ m/s. (use g = 10 m/s²)
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4.94
B = 2m, y2 = 0.8m, V2 = 1 m/sF2 = V2 √gy2 = 1 = 0.35 √10 × 0.8 y1 = - 1 + 1 √1 + 8F²2 y2 2 2 ⇒ y1 = - 1 + 1 √1 + 8 × (3.5)²2 = 0.203 0.8 2 2
∴ y1 = 0.8 × 0.203 = 0.162 m
Q = AV2
= B.y2 × V2
= By1 × V1
⇒ 0.8 × 1 = 0.162 × V1
⇒ V1 = 4.94 m/sCorrect Option: B
4.94
B = 2m, y2 = 0.8m, V2 = 1 m/sF2 = V2 √gy2 = 1 = 0.35 √10 × 0.8 y1 = - 1 + 1 √1 + 8F²2 y2 2 2 ⇒ y1 = - 1 + 1 √1 + 8 × (3.5)²2 = 0.203 0.8 2 2
∴ y1 = 0.8 × 0.203 = 0.162 m
Q = AV2
= B.y2 × V2
= By1 × V1
⇒ 0.8 × 1 = 0.162 × V1
⇒ V1 = 4.94 m/s
- Irrigation water is to be provided to a crop in a field to bring the moisture content of the soil from the existing 18% to the field capacity of the soil at 28%. The effective root zone of the crop is 70 cm, If the densities of the soil and water are 1.3 g/cm3 and 1.0 g/cm³ respectively, the depth of irrigation water (in mm) required for irrigating the crop is _________.
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91
Depth of irrigation water required, dwdw = g d.(fc - w) gw = 1.3 × (70 × 10)(0.28 - 0.18) = 91 mm 1 Correct Option: A
91
Depth of irrigation water required, dwdw = g d.(fc - w) gw = 1.3 × (70 × 10)(0.28 - 0.18) = 91 mm 1
- An incompressible fluid is flowing at a steady rate in a horizontal pipe. From a section, the pipe divides into two horizontal parallel pipes of diameters d1 and d2 (where d1 = 4d2) that run for a distance of L each and then again join back to a pipe of the original size. For both the parallel pipes, assume the head loss due to friction only and the Darcy-Weisbach friction factor to be the same. The velocity ratio between the bigger and the smaller branched pipes is _______.
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2
d1 = 4d2
Darey-wers bach friction factor is same (f)flv²1 = flv²2 2gd1 2gd2 ⇒ v²1 = v²2 d1 d2 ⇒ v²1 = d1 v²1 d2 ⇒ v²1 = d1 = 4d2 = 4 v²1 d2 d2 ∴ v1 = √4 = 2 v2 Correct Option: D
2
d1 = 4d2
Darey-wers bach friction factor is same (f)flv²1 = flv²2 2gd1 2gd2 ⇒ v²1 = v²2 d1 d2 ⇒ v²1 = d1 v²1 d2 ⇒ v²1 = d1 = 4d2 = 4 v²1 d2 d2 ∴ v1 = √4 = 2 v2
Direction: A rectangular open channel needs to be designed to carry a flow of 2.0 m³/s under uniform flow conditions. The Manning’s roughness coefficient is 0.018. The channel should be such that the flow depth is equal to half the width, and the Froude number is equal to 0.5.
- Keeping the width, flow depth and roughness the same, if the bed slope of the above channel is doubled, the average, boundary shear stress under uniform flow conditions is
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τ = ωRs
S1 = 250 = 0.0042; R = y/2 = 0.418
τ = 9810 × 0.418 × 0.0042 = 17.2 N/m².Correct Option: D
τ = ωRs
S1 = 250 = 0.0042; R = y/2 = 0.418
τ = 9810 × 0.418 × 0.0042 = 17.2 N/m².
