Download EXAMPLES TEST 2 PROBLEMS

EXAMPLES TEST 2 PROBLEMS
1. Draw the approximate hydraulic grade line (piezometric level) for the pipe system
below if the pressure at C is equal to atmospheric pressure. Include local losses at pipe
exits, entrances, and valves.
2. A heat exchange system pumps water continuously from a lake in a 500 m pipe (D =
250 mm, ks = 0.025 mm) and heat exchanger (VVX). After this the water is discharged to
the lake again. The pump characteristics are shown in the table. The heat exchanger can
be treated as a local loss from a flow point of view with a loss coefficient KVVX= 15. The
sum of all other local losses is 5V2/2g. What is the flow in the pipe? Assume ν = 1  10-6
m2/s.
Pump characteristics:
3. A circular tunnel, 3 m in diameter and with a friction loss coefficient f = 0.01,
connects a reservoir and a hydropower station. The tunnel is 5 km long and there is a socalled pressure tower 0.5 km from the station (the pressure tower protects the turbine
against hydraulic hammer effects due to quick changes in flows and acts as a piezometer
under stationary conditions). The water surface in the reservoir is 60 m above the outflow
from the turbine where water is discharged in to atmospheric pressure.
a) Determine at what level the water in the pressure tower is at when there is no flow in
the tunnel (valve closed).
b) Determine the flow in the tunnel and the water level in the pressure tower when
stationary flow exists and when the pressure drop over the turbine (from end of tunnel
before the turbine to the outflow from the turbine) is 45 m. Assume velocity at outflow
equal to the tunnel velocity. Neglect all local losses except that for the turbine.
4. Water flows from reservoir A, with a constant surface area equal to 100 m2, to
reservoir B with a constant surface area equal to 50 m2, through a rectangular (0.2 x 0.3
m) pipe with length L = 200 m, and with a friction coefficient f = 0.025. The sum of all
local losses through the pipe is 4.0 (V2/2g). The water surface in reservoir A is initially at
+12 m and at +4 m in reservoir B. Determine the time it takes to lower the water level in
reservoir A to +10 m. Do not forget that the water level in reservoir B will continuously
change during this period of time. Assume that the stationary version of the energy
equation can be used to describe the flow in the pipe, that is, the water acceleration can
be neglected. The is no inflow to reservoir A and no outflow from reservoir B.
5. The irrigation system in the below figure is connected to a pipe with large diameter
and a constant inner pressure of p0 = 300 kP. The system is located horisontally.
Determine the water flows Q1, Q2, Q3, and Q4 for given system. K stands for the total
(added) local loss coefficient (including valve) for each pipe.
6. Treated waste water is pumped with two identical pumps (see pump curve for one
pump below) in parallel from a reservoir through a pipe to the sea according to figure
below. A valve after the pumps is used to control the flow. If the pressure gage located
half way along the pipe shows a pressure of 50 kPa for a specific valve opening,
determine the flow in the pipe and the local loss coefficient for the valve Kv. The length
of pipe, diameter, and roughness are 2 km, 300 mm, and 0.3 mm, respectively. The
pressure gage is located at a distance of 2 km from the pipe discharge point in the sea.
The temperature of the water is 20oC. Neglect all local losses except over the valve.
7. Freshwater to two cities (corresponding to reservoir B and C) is transported from a
lake (A) through three pipes, according to below. If the flow through pipe 2 when the
valve is completely open (Kvalve = 0) is reduced by 50% by partly closing the valve, what
will be the flow increase to reservoir C. Data for the three pipes are given below. Note
that all pipes have rectangular transect areas. Assume raw turbulent flow and neglect all
local losses, except for the partly closed valve in pipe 2.
8. The flow over the dam in the figure is 2.0 m3/s and width m (in to the
paper). How large is the depth y2 downstream the hydraulic jump? Assume
that the energy loss is negligible over the dam crest.
9. Water flows over a hump in a channel, according to below. The water depth y2 over the
hump is 0.6 m. The hump height over the channel bottom is 0.4 m. Assume wide
rectangular channel and that energy losses over the hump is negligible.
a) Determine the flow per width meter in the channel.
b) Determine the water depth y1 in the channel upstream the hump.
10. A uniform flow in a wide channel (Manning´s n = 0.015) with bottom slope 0.02o
flows over a 10 cm high bump. The result is a somewhat lower water depth over the
bump. If the water depth over the bump y2 = 50 cm determine the flow pr width meter in
the channel.
11. Water is discharging at normal water depth in a rectangular concrete channel
(Manning´s n = 0.013) that is 12 m wide. Downstream there is a dam-shaped weir
damming the water and thus increases the water level over a distance L, see figure below.
The discharge is 126 m3/s and the channel bottom slope is 0.00086. The water depth y0
just upstream the weir is 4.55 m. Determine the distance L from the weir to the point
upstream where the water depth corresponds to natural depth (yn).
12. Water flows in a rectangular concrete channel (Manning´s n = 0.013) that is 2 m
wide. The water flow is 0.7 m3/s. Determine the water profile along the channel.
13. The pole in the figure is a cylinder with the diameter 100 mm. A wind with 15 m/s
velocity blows around the pole. The air temperature is 0oC. Determine the drag force
around the base of the pole (at soil surface level). Neglect boundary effects.
14. A sphere with diameter 70 mm and weight 350 g sinks through water with a constant
velocity due to gravitation. Determine the velocity. The water temperature is 20oC.