RIB-R T11 RIB Rank Improvement Batch Session 18-1 S.No. : 118_SK CIVIL ENGINEERING Engineering Hydrology ANSWERS 1. (b) 7. (c) 1. (c) 1. (b). (d). (c) 8. (a) 1. (a). (b). (c). (a). (d) 1. (c) 1. (a) 7. (b). (a) 1. (c) 1. (d). (d) 8. (a). (a) 11. (c) 17. (b). (c). (c). (a) 1. (a) 18. (b). (c). (c) Detailed Explanations 1. (b) Discharge 1hr 1hr Q (m /s) t t T (hr) Time. (c) For -hr UH, the base time will increase, hence peak will go down. Equilibrium Discharge, Q (ordinates of -hr UH) m /s at hr
Civil Engineering. (a) Since variation is more than 1%, 1 1 1 1 P x + + 1 1 1 8. cm. (a) Q equilibrium.78 A T 1.78 cumecs. (a) Main stream Tributaries Tributaries Water Shed line Main stream (Fan Shaped Catchment) (Fern Leaf Catchment) 7. (c) The limiting case of a UH of zero duration is known as IUH (Instantaneous Unit Hydrograph). The ordinate of one IUH at any time t is the slope of S-curve of intensity 1 cm/hr. 8. (a) Isopleth is a line on a map connecting points having same numerical values of a certain quantity such as population figure or geographical measurement. Isobars are contour lines that connects different points with same constant pressure. Isochrones are lines on a map connecting points relating to equal time of travel of surface runoff or equal time of concentration. 11. (c) Peak of DRH 1 1 1 m /s P mm, φ mm/hr n P φ t 1 mm cm Peak of 1 hr. UH 1 m /s 1. (a) n + cm For DRH, ( O) (1 + 7 + + 7 + 7 + 1 + 1) 7 1 n. Ot A A. 1 1 7. km
7 1. (c) P 1 cm 1 1 1 1 1 m R 1 m /s 1 m R Runoff coefficient. P 1 1. (a) Time (hr) 8 1 - h UH (m /s) S-curve addition S-curve Offset S-curve y - h UH ( y /) 1...7 1. (c) (i) Mean rainfall, ( P ) P 8 + + + mm n P P (ii) Standard deviation, σ 1. n 1 (iii) Coefficient of variation, c v 1 σ 1 1. 8. P c v 8. (iv) Optimum number of rain gauges, (N ) 8Nos 1 (v) 1. (d) Additional gauges required to be installed 8 Existing gauges 8 Time (1) Total Stream flow in cumecs () Base flow in cumecs () Direct run off column () () 8 1 1.1. 7. 1. 8.8 7.. 1.7.... Using Simpson s rule, the area enclosed by this discharge hydrograph st H 1 + last ordinate + Even ordinates + odd ordinates +. (...) (1.7.) + + + + + 1 m
8 Civil Engineering 17. (b) 1 Depth of water in the hydrograph 1 Rainfall cm Runoff.8 cm Infiltration including basin recharge.8 1.1 cm t r hr (given) φ index 1.1. cm/hr.8 1 m or.8 cm.8 Loss Rainfall Runoff.18 m1.8cm 1 8. 1 Rate of loss 1.8.cm/hr 18. (b) The probability of occurrence of an event (x x T ) at least once over a period of n successive years is called the risk, R. Hence, risk is given by R 1 ( Probability of occurence of the event x xt in n years) where, n 1 1 1 1 1 1.7. T T Return period years n Expected life years 1. (b) Thiessen Polygon Method: In this method, the rainfall recorded at each station is given a weightage on the basis of an area closest to the station.. (b) PA P avg 1 1 + P A +... + PA n n A + A +... + A 1 n where, P 1, P,... P n are the rainfall data of areas A 1, A... A n. Rainfall intensity (cm/hr) 1 8 7 1 φ index cm/hr 1 7 1 Time (min) Hatched portion shows the total runoff and dotted portion shows the total infiltration.
1 1 1 8 + 7.cm Total runoff ( 8 ) + ( 7 ) Total precipitation 1 1 1 1 1 1 + + 8 + 7 + 1. + 1. W-index. (c) Let the peak of the UH be Q P. The UH can be shown as 1 + + 8 + 7 + 1. + 1..7 cm Total precipitation Runoff.7. Duration of rainfall in hr /.8 cm/hr.8 cm/hr Discharge Q p 7 hr Area of DRH gives the volume of rainfall, 1 7 QP 1 7 1 1 Q p m /s Peak of DRH n peak of UH m /s Time. (d) Total rainfall. + 1.8 +.. cm Infiltration.. cm Excess rainfall duration, t e hrs. φ-index.. cm/hr This value being more than. cm/hr, The excess rainfall duration will reduce by hrs. t e hrs. Infiltration (1.8 +.).7 cm φ-index.7.7 cm/hr
1 Civil Engineering. (c) 7. (b) 1 8 + + 1 + + 7 x ni 8 cm n The standard deviation of the rainfall is given by σ σ 1.81 ( x x) n 1 σ C V 1 1.7 x N C V 1.7 1.8 11 Thus, additional number of rainguages 11 First hour: P excess Second hour: P excess () + 1( ) + 11 1 17. mm ( ) + + ( ) 1( ) 11 1 ( ) + + ( ) 8 1(8 ) 118 1 Third hour: P excess Total rainfall excess for the hour storm 17. +. +. 18. mm 8. (a) The calculations are tabulated below: Time (hr) FH (m /s) Base Flow (m /s) DRH (m /s) Col. (1) Col. () Col. () Col. () 1 1 1 8 7 8 7 8 1 1 Σ O Base flow m /sec Now, direct runoff depth, DRD. Σ O t A where ΣO m /s; t 1 hr; A km DRD. 1. cm. mm. mm
11. (c) Rainfall Intensity (cm/hour).. 8. 7.... φ. cm/hour. (c) 1 1 18 1 Duration (minutes) Rainfall excess is shown by hatched area. Total rainfall P (. +. + 8. + 7. +. +. +. +.). cm Total rainfall excess R [(..) + (8..) + (7..) + (..) + (..) ] 1 ( + + + 1. + 1.). cm P R.. W-index. cm/hour t Time hr 1 8 Inflow m /s 1 7 78 7 7 Q initial 1 m /s k 18 hours x. kx < t < k 18. < t < 18 t 1 hrs Using Muskingham equation C C 1 C kx +. t 18. +. 1 k 1 +. t 18 1. +. 1. ( x) ( x) kx +. t 18. +. 1 k 1 +. t 18 1. +. 1.1 k(1 x). t k(1 x) +. t 18 1.. 1 18 1. +. 1.