# CVE 372 HYDROMECHANICS EXERCISE PROBLEMS

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1 VE 37 HYDROMEHNIS EXERISE PROLEMS 1. pump that has the characteristic curve shown in the accompanying graph is to be installed in the system shown. What will be the discharge of water in the system? Take ν = 10-6 m /s. L = 15 m D = 0 cm f = 0.0 P 5 m L = 85 m D = 0 cm f = m 3 m DTUM Pump urve H (m) Q (l/s) 1

2 . With a flow of 450 l/s of water, find the head loss and the division of flow in the pipes from to. Take ν = 10-6 m /s and ε = 0.1 mm for all pipes. L = 600 m D = 60 cm L = 1000 m D = 35 cm L = 600 m D = 30 cm D L = 1000 m D = 40 cm L = 100 m D = 75 cm 3. ssuming f = 0.00, determine the discharge in the pipes. Neglect minor losses. Take ν = 10-6 m /s. 50 m 5 m L = 3000 m D = 5 cm 3 m L = 100 m D = 0 cm L = 500 m D = 30 cm 0 m

3 4. ssuming f = 0.00, determine the discharge in the pipes. Neglect minor losses. Take Q = 60 l/s for the first trial value. Stop iteration when Q < 3 l/s. Take ν=10-6 m /s. 00 l/ L = 100 m D = 15 cm L = 150 m D = 0 cm 50 l/s L = 150 m D = 0 cm 00 l/s D L = 50 m D = 10 cm 50 l/s 5. Three reservoirs are connected with smooth pipes at a junction point. It is known that flow direction in pipe- is from reservoir to the junction, and the discharge of pipe-1 is equal to the discharge of pipe-, Q 1 = Q. For pipe characteristics given in the table below, compute the water surface elevation in reservoir. (ν = 1.0 x 10-6 m /s ) z = 37 m 1 J z = 360 Pipe D(m) L(m) z =? ns.:z c =347.7 m 3

4 6. ssuming points,, D and E lie on the same plane (z = z = z D = z E ), determine the direction and magnitude of the discharge in each pipe in the network shown in the figure. (Use at least two iterations) Given: K = 3, K 3 = 5, K 4 = and K 5 = 5 where K has been defined as: h f = z = 180 m ns. Q =9.07 lt/s Q 3 =14.07 lt/s Q 4 =40.93 lt/s Q 5 =5.93 lt/s [1] Reservoir [] 15 lt/s [3] E 0 lt/s [4] [5] D 35 lt/s 7. ompute flow rate for the pipeline shown below. lso determine Hp values of each pump in the system. Pump characteristic head- discharge curves for the pumps are given in the table below. Use D = 0.5 m, L = 1000 m, assume that f = 0.0. Q ( lt/s) (H p ) 1 (m) (H p ) (m) m 100 m P1 P L total = 1000 m D = 0.5 m ns.: Q=138 lt/s Hp 1 =35 m Hp =18 m 4

5 8. viscous oil with a specific gravity, SG=0.8 and a viscosity of Pa.s flows from tank to tank through the six rectangular slots indicated in figure. If the total flowrate is 3 lt/s and minor losses are negligible, determine the pressure in tank. ssume hydraulically smooth flow. Each slot 1cm x 1cm Same a 6 m Section a- a ns. P =131 kpa 9. For H=30 m in the figure below, a) Find the discharge through each pipe b) What will be the equivalent length of a pipe having a diameter of 10 mm with =0.0018m replaced instead of pipes 1 and? Neglect minor losses, ν water =1x10-6 m /s Pipe L(m) D(mm) (m) H=30 m 3 ns. Q 1 =14.4 lt/s Q =63.8 lt/s Q 3 =77 lt/s 10. For the system given in the figure, find the elevation of Reservoir D and the flow direction in pipe 6. Neglect minor losses. El 80 m 1 P El 90 m 3 4 El 60 m 5 6 El =? D Pipe L (m) D(mm) f Q 1 = 0.35m 3 /s Hp = 8m ns. Q =350 lt/s Q 3 =71 lt/s Q 4 =61 lt/s Q 5 =549 lt/s H p =34.7 m 5

6 11. Find the discharge in each link using the given initial distribution by making iterations and pressure drop between points O and if they have the same elevation. 5 lt/min? 6 lt/min D K =K D =K O =K OE K =K DE K O =3K K =K K O =30 min /dm lt/min 7 lt/min O 0 E 1. Two water reservoirs with a difference in elevation of 5m are connected by 800m of commercial steel pipe. The roughness height of the pipe is 0.18 mm. What size pipe must be used to convey 100 lt/s? Neglect minor losses, ν water =1x10-6 m /s. ns. D=30 cm 13. fluid of specific gravity 0.96 flows steadily in a long, vertical.5 cm diameter pipe with an average velocity of 0.15 m/s. a) If the pressure is constant throughout the fluid, what is the dynamic viscosity of the fluid? b) Determine the shear stress on the pipe wall. ( ρ w = 1000 kg/m 3, g = 9.81 m/s ) D = 0.05 m L (1) V = 0.15 m/s SG = 0.96 () 6

7 14. smooth plastic, 10-m long garden hose with inside diameter of 15 mm is used to drain a pool as shown in the figure. Including both friction and minor losses, determine the flowrate from the pool. (ν = 1 x 10-6 m /s) 0. m K ent = m 15. In the following pipe system, water discharge in pipe 1 is given as Q 1 =1. m 3 /s. The upstream and downstream reservoir water surface elevations are known, and they are z =100 m, and z =80 m, respectively. Relevant pipe data are provided in the table below. Determine the diameter in pipe 3. Velocity head at the junction and minor losses in the system will be neglected. (ν = 1 x 10-6 m /s) z =100 Pipe L (m) D (mm) ε (mm) ? 4.4 (1) Q 1 =1. m 3 /s z =80 m () J (3) 7

8 16. The water surface elevations in the three reservoir system are shown in the figure. In addition, the pipe data are provided in the table below. The discharge in pipe D is 100 lt/s. Use f = 0.0 for all pipes. a) Determine the minor loss at the valve, h valve, and minor loss coefficient, K valve. (Note: Neglect all other minor losses.) b) Draw the energy gradeline for the system. 100 m 100 m Pipe L (m) D (mm) D D D Q D D 75 m valv 17. Water flows from the reservoir through a pipe as shown in the figure. a) alculate the discharge by assuming that flow is irrotational and inviscid. b) alculate the discharge and pump head by considering all the losses in the system 30 m K ent =1 P L=50 m D=0 cm k s =0.0 cm K elbow =1.5 3 m K elbow =1.5 K nozzle =0.75 8

9 18. Water flows at a rate of m 3 /s from a lake as shown in the figure below. The pipe is 100 m long and the diameter of the pipe is 10 cm and the roughness height is 0.0 cm. a) Is the device inside the building a pump or a turbine? Explain. b) Determine the power of the device if the efficiency of the device is 86 %. 160 m Power house 150 m Pipe properties D=10 cm L=100 m ε = 0.0 cm 19. The pump in the figure has the performance characteristics shown. The mechanical energy loss in the piping and fittings in the suction and discharge pumping is given by V h L = K where V is the average fluid velocity in the pipe and K = 10. Find g the flow rate through the pump and power supplied by the pump to the fluid. D 1 =100 mm Pump D =100 mm Q=? 15 m H P (m) Q (m 3 /s) 9

10 0. In a chemical processing plant a liquid is pumped from an open tank through a 0.1-m-diameter vertical pipe into another open tank as shown in the figure below. valve is located in the pipe, and the minor loss coefficient for the valve as a function of the valve setting is shown in the figure below. The pump head-capacity relationship is given by the equation: H p = x10 3 Q with H p in meters when Q is in m 3 /s. ssume the friction factor f = 0.0 for the pipe, and all minor losses, except for the valve, are negligible. The fluid levels in the two tanks can be assumed to remain constant. Determine: (a) the flowrate with the valve wide open. (b) the required valve setting (percent open) to reduce the flowrate by 50 %. 3 m valve D=0.10 m 30 m P Q K L (Open) Percent valve setting (losed 10

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