TUTORIAL 3: Hydrodynamics – Continuity & Energy Eqn, and Their Applications EC110/UiTMKS2
1. The diameters of a pipe at the sections 1 and 2 are 10 cm and 15 cm respectively as shown in Figure
Q1. Find the discharge through the pipe if the velocity of water flowing through the pipes at section 1 is
5 m/s. Find also the velocity at section 2.
1 2
Figure Q1
2. A 30-cm diameter pipe, conveying water, branches into two pipes of diameters 20 cm and 15 cm
respectively. If the average velocity in the 30 cm diameter pipe is 2.5 m/s, find the discharge in this
pipe. Also determine the velocity in 15 cm pipe if the average velocity in 20 cm diameter pipe is 2 m/s.
v2 = 2 m/s
v1 = 2.5 m/s
d1 = 30 cm d2 = 20 cm
v3 = ?
d3 = 15 cm
Figure Q2
3. Water flows through a pipe AB 1.2 m diameter at 3 m/s and then passes through a pipe BC 1.5 m
diameter. At C, the pipe branches. Branch CD is 0.8 m in diameter and carries one-third of the flow in
AB. The flow velocity in branch CE is 2.5 m/s. Find the volume rate of flow in AB, the velocity in BC, the
velocity in CD and the diameter of CE.
D
A B
C
E
Figure Q3
4. Figure Q4 shows pipes 2 and 3 branching from pipe 1. If pipe 2 takes 30% of the total discharge, what
are the values of discharge and mean velocity in each pipe? If the diameter of pipe 1 is increased by
50% while maintaining the discharge, how would this change affect the velocity in pipe 2 and 3?
Assume that the discharge distribution in pipe 2 and 3 remain same.
FigureQ4
bcbsept19
, TUTORIAL 3: Hydrodynamics – Continuity & Energy Eqn, and Their Applications EC110/UiTMKS2
5. Oil flows through a pipeline which contracts from 450 mm diameter at A to 300 mm diameter at B and
then forks one branch being 150 mm diameter discharging at C and the other branch, which has a 225-
mm diameter discharging at D as shown in Figure Q5. If the velocity at D is 3.6 m/s and velocity at A is
1.8 m/s, compute the discharges at C and D and the velocities at B and C.
Figure Q5
6. When 0.3 m3/s of water flows through a 175-mm constriction in a 350-mm horizontal pipeline, the
pressure at a point in the pipe is 300 kPa, and the head loss between this point and the constriction is 2
m. Calculate the pressure in the constriction. Refer to Figure Q6.
Flow
direction
1 2
Figure Q6
7. Water flows in a pipeline. At a point in the line where the diameter is 200 mm, the velocity is 3.6 m/s
and the pressure is 345 kPa. At a point 12 m away, the diameter reduces gradually to 100 mm.
Calculate the pressure here when the pipe is (a) horizontal, and (b) vertical with flow downward.
8. For the pipeline shown in Figure Q8, calculate the discharge and the pressures at A, B, C and D if
water flows out as a jet through a 50-mm diameter nozzle.
C
B 1.5 m
3.6 m
D
6m
A 2.4 m
Figure Q8
9. Water flows from reservoir A, at a rate of 20 L/s to premises B and C through pipes of different
diameters as shown in Figure Q9. At point D water is abstracted, at a rate of 10 L/s, from the 150-mm
diameter pipe. If the velocity of flow in the 50-mm diameter pipe is 3.0 m/s, calculate;
a. The flow rate in the 35-mm diameter pipe
b. The pressure in the 50-mm diameter pipe at E, a point which is located 10 m below the water
surface of reservoir A
bcbsept19
1. The diameters of a pipe at the sections 1 and 2 are 10 cm and 15 cm respectively as shown in Figure
Q1. Find the discharge through the pipe if the velocity of water flowing through the pipes at section 1 is
5 m/s. Find also the velocity at section 2.
1 2
Figure Q1
2. A 30-cm diameter pipe, conveying water, branches into two pipes of diameters 20 cm and 15 cm
respectively. If the average velocity in the 30 cm diameter pipe is 2.5 m/s, find the discharge in this
pipe. Also determine the velocity in 15 cm pipe if the average velocity in 20 cm diameter pipe is 2 m/s.
v2 = 2 m/s
v1 = 2.5 m/s
d1 = 30 cm d2 = 20 cm
v3 = ?
d3 = 15 cm
Figure Q2
3. Water flows through a pipe AB 1.2 m diameter at 3 m/s and then passes through a pipe BC 1.5 m
diameter. At C, the pipe branches. Branch CD is 0.8 m in diameter and carries one-third of the flow in
AB. The flow velocity in branch CE is 2.5 m/s. Find the volume rate of flow in AB, the velocity in BC, the
velocity in CD and the diameter of CE.
D
A B
C
E
Figure Q3
4. Figure Q4 shows pipes 2 and 3 branching from pipe 1. If pipe 2 takes 30% of the total discharge, what
are the values of discharge and mean velocity in each pipe? If the diameter of pipe 1 is increased by
50% while maintaining the discharge, how would this change affect the velocity in pipe 2 and 3?
Assume that the discharge distribution in pipe 2 and 3 remain same.
FigureQ4
bcbsept19
, TUTORIAL 3: Hydrodynamics – Continuity & Energy Eqn, and Their Applications EC110/UiTMKS2
5. Oil flows through a pipeline which contracts from 450 mm diameter at A to 300 mm diameter at B and
then forks one branch being 150 mm diameter discharging at C and the other branch, which has a 225-
mm diameter discharging at D as shown in Figure Q5. If the velocity at D is 3.6 m/s and velocity at A is
1.8 m/s, compute the discharges at C and D and the velocities at B and C.
Figure Q5
6. When 0.3 m3/s of water flows through a 175-mm constriction in a 350-mm horizontal pipeline, the
pressure at a point in the pipe is 300 kPa, and the head loss between this point and the constriction is 2
m. Calculate the pressure in the constriction. Refer to Figure Q6.
Flow
direction
1 2
Figure Q6
7. Water flows in a pipeline. At a point in the line where the diameter is 200 mm, the velocity is 3.6 m/s
and the pressure is 345 kPa. At a point 12 m away, the diameter reduces gradually to 100 mm.
Calculate the pressure here when the pipe is (a) horizontal, and (b) vertical with flow downward.
8. For the pipeline shown in Figure Q8, calculate the discharge and the pressures at A, B, C and D if
water flows out as a jet through a 50-mm diameter nozzle.
C
B 1.5 m
3.6 m
D
6m
A 2.4 m
Figure Q8
9. Water flows from reservoir A, at a rate of 20 L/s to premises B and C through pipes of different
diameters as shown in Figure Q9. At point D water is abstracted, at a rate of 10 L/s, from the 150-mm
diameter pipe. If the velocity of flow in the 50-mm diameter pipe is 3.0 m/s, calculate;
a. The flow rate in the 35-mm diameter pipe
b. The pressure in the 50-mm diameter pipe at E, a point which is located 10 m below the water
surface of reservoir A
bcbsept19
