MZUZU UNIVERSITY FACULTY OF ENVIRONMENTAL SCIENCES

DEPARTMENT OF WATER RESOURCES MANAGEMENT AND DEVELOPMENT

BACHELOR OF SCIENCE IN WATER RESOURCES MANAGEMENT AND DEVELOPMENT

Level 3

DIFFERED EXAM 2013

COURSE NAME HYDRAULICS I COURSE CODE WRMD3604

Instructions

1. This paper contains seven questions, please check. 2. Answer any five questions. 3. Do not attempt more than five questions. 4. Answer each question on a separate sheet 5. Each question carries a total of 20 marks, please check. 6. Marks are indicated against each question.

QUESTION ONE

FIG 1: WATER DISTRIBUTION SYSTEM

Figure 1 shows the layout of a water distribution system with a reservoir, inflow and outflow as shown.

(a) Determine the distribution of flow in the network. (10 marks) (b) Also determine the elevation of the hydraulic grade line at points 1 and 5 if the

reservoir elevation is 10m. (10 marks)

Pipe identities, lengths and diameters are indicated in table 1 below. Take roughness factor to be 0.06mm for all the pipes. Apply three iterations for each loop. (20 marks)

Table 1: Pipe Discription

Note: There is no flow in and out of the reservoir.

QUESTION TWO

(a) Show that in an elastic pipe under very high surge conditions the velocity of the

shock wave is given by the formula where:-

C =shock wave velocity in m

= the density of water

K = the bulk modulus of water

D = is the diameter of the pie in m

E = is Youngs Modulus for the pipe material

e =is pipe thickness in m (10 marks)

(b) A water supply main is 3Km long and carries water. The velocity of the water is 2.5m/s. Calculate the surge pressure for instantaneous closure if K=2.13x109 N/m2. (10 marks)

QUESTION THREE

(a) Show that for a sharp crested weir, ideal flow over the weir is given by the formula;-

2

where:

Q = flow in m3/s

b =crest width

g =acceleration due to gravity m/s/s

H =is water head in m (7 marks)

(b) A long channel 1.5m wide terminates in a full width rectangular weir whose crest height is 300mm above the stream bed. If the measuring station is recording a depth of 400mm above the weir crest, estimate the discharge:

i. Assuming a flow with a negligible velocity of approach (Take Cd=0.7) ii. Including velocity of approach (taking =1.1 and Cd=0.7)

=Coriolis coefficient

Cd = Discharge coefficient. (13 marks)

QUESTION FOUR

(a) A cast iron pipe 20cm in diameter and with 15mm thick walls is carrying water when the outlet is suddenly closed. If the design discharge is 40l/s, calculate the water hammer pressure rise if ;-

i. The pipe wall is rigid. ii. The longitudinal stress is negligible. iii. The pipe has expansion joints throughout its length (10 marks)

(b) A pump installed in a 15cm, 300m long pipeline to pump 0.06m3/s of water at 200C. The elevation difference between the supply reservoir and the receiving reservoir is 25m. If the pump has a 18cm impeller intake diameter, a cavitation parameter =0.12 and experiences a total head loss of 1.3m on the suction side, determine the maximum allowable distance between the pump intake and the water surface elevation in the supply tank. Assume the pipeline has CHW =120 where C is Hazen Williams Coefficient of Friction. (10 marks)

QUESTION FIVE

(a) Show that in estimating parameters for nodal analysis of a water distribution network an error H

where H is head in m, q is flow and hf is frictional

head loss. (7 marks)

(b) Four pipes from reservoirs meet at a common point, J. The parameters describing the system are indicated in table 2 below.

Pipe Reservoir Level (m above datum)

Pipe length (m) Diameter (m) f

A 100 3000 1.5 0.004 B 110 6000 1.0 0.007 C 80 3000 1.0 0.006 d 40 10000 2.0 0.004

Determine the flow in each pipe and the pressure at J in m (13 marks)

QUESTION SIX

(a) Show that the movement of water level above and below the neutral of the surge tank imitates a damped simple harmonic motion after uniform closure of the valves to the turbines of the hydropower plant. (10 marks)

(b) A simple surge tank 8m in diameter is located at the downstream end of a 1500m long pipe, 2.2m in diameter. The head loss between the upstream reservoir and the surge tank is 15.3m when the flow rate is 20m3/s. Determine the maximum elevation of water in the surge tank if the valve downstream suddenly closes. (10 marks)

QUESTION SEVEN

(a) With the help of an example explain the following principles and how they are applied in the design of hydraulic structures;-

i. Geometric Similarity. ii. Kinamatic Similarity iii. Dynamic Simulitude. (7 marks)

(b) A 100mm diameter pump, which is driven by a synchronous electric motor, has been tested with the following results.

i. Power supplied to pump =3.2kW ii. Pump speed =1450 rev/min, head =12.9m, discharge=20l/s iii. Efficiency=79%; fluid is water at 180C.

A geometrically similar pump is required to deliver 100l/s against a head of 20m. The new pump will be driven by a synchronous motor. The speeds may be either 960 rev/min or 1450 rev/ min. Calculate the principal characteristics (size, speed and power) of the new machine. Calculate also the specific speed, Ns. (13 marks)

END OF QUESTION PAPER