MANILA: Room 206, JPD Building, CM Recto Avenue, Manila

CEBU: 4/F J. Martinez Bldg., Osmeña Blvd., Cebu City

Telephone Number: (02) 516-7559 (Manila) E-Mail: buksmarquez1 @yahoo.com
(032) 254-9967 (Cebu)
REVIEW MODULE – HYDRAULICS 3 [Relative Equilibrium of Fluids, Fundamentals of Fluid Flow and Fluid Flow Measurements]
RELATIVE EQUILIBRIUM OF LIQUIDS- RECTILINEAR MOTION SITUATION. An open tank is filled with gasoline (s = 0.80) and is accelerated
A. Horizontal Motion vertically at 5 m/s2. Determine the pressure at a point 3 m below the surface if the
motion is:
a 6. Upward with a positive acceleration.
W=mg 7. Downward with a negative acceleration.
REF=ma
ϴ
N RELATIVE EQUILIBRIUM OF LIQUIDS- ROTATIONAL MOTION
ϴ D. Rotational Motion
Mass of liquid MEGAREVIEW

A W=mg
ϴ N
W=mg
M 2
h x dx
dy
CF=mω x
y
2
B CF=mω x
ϴ ϴ
ϴ N
N W=mg 𝑎
tan 𝜃 = tan 𝜃 =
𝐶𝐹
𝑔 𝑊
𝜔2𝑥
REF=ma r tan 𝜃 =
𝑔
𝑑𝑦
= tan 𝜃
𝑑𝑥
SITUATION. An open tank 2 m by 3 m horizontal section weighs 3.6 kN and contains 𝜔2𝑥2
𝑦=
water to a depth of 1 m. It is acted upon by an unbalanced force of 16 kN parallel to 2𝑔
a pair of sides.
1. What must be the least height of the tank so that no water will spill out? SITUATION. An open cylindrical tank having 0.30 m radius and a height of 1.20 m
2. What is the force acting on the front end of the tank? is 3/4 full of water. Determine the angular speed in rpm if:
3. If the acceleration is increased to 4 m/s2, how much water will pour out of the 8. The water will just touch the rim.
tank? 9. The vortex will just touch the base.
4. If the tank in the situation is closed, what will be the force acting on the back 10. The base is uncovered within 15 cm from the vertical axis.
face of the tank?
SITUATION. A closed cylindrical vessel 1.2 m in diameter and 2.1 m high is filled
with water to a height of 1.6 m. The air inside the tank is under a pressure of 120
B. Inclined Motion
kPa. If the vessel is rotated at 200 rpm,
11. Determine the maximum and minimum pressure at the base.
12. How much area at the bottom is uncovered?
W=mg
13. A horizontal tube, 2.5 m long and 6 mm in diameter, is filled with water under
a pressure of 70 kPa and closed at both ends. If rotated in a horizontal plane
about an axis 30 cm from one end at the rate of 2π rad/s, what will be the
pressure at the outer end?

FUNDAMENTALS OF FLUID FLOW (Fluids in Motion)

Discharge/Flow Rate – amount of fluid passing through a section per unit of time
Volume Flow Rate
𝑄 = 𝐴𝑉
Mass Flow Rate
𝑀 = 𝜌𝐴𝑉
𝑎
ϴ W=mg tan 𝜃 = Weight Flow Rate
N 𝑔 𝑊 = 𝛾𝐴𝑉

α REFy SITUATION. A gas flows through a circular conduit. At one point along the conduit,
REFx the diameter is 100 mm, the velocity is 7.55 m/s, and the gas’s mass density is (for
its particular pressure and temperature) 1.09 kg/m3. At a second point, the diameter
is 250 mm, and the velocity is 2.02 m/s.
5. A vessel containing oil is accelerated on a plane inclined 10° with the 14. Find the mass flow rate of the gas
horizontal at 1.5 m/s2. Determine the inclination of the oil surface when the 15. Find the mass density at the second point.
motion is downwards?
ENERGY and HEAD
Kinetic Energy – the ability of the fluid mass to do work by virtue of its velocity.
C. Vertical Motion
Potential Energy – the energy possessed by the fluid by virtue of its position or
a elevation with respect to a datum line or by virtue of the pressure experience by the
fluid at that point.
Head – the amount of energy per pound or Newton of fluid
Elevation Head, z
REF=ma
Pressure Head, p/γ
Velocity Head, v 2 /2g
W=γV ±𝑎
𝑝 = 𝛾ℎ (1 ± )
h 𝑔 BERNOULLI’S ENERGY EQUATION
A (Area) No Head Added or Lost:
p1 (v1 )2 p2 (v2 )2
F=pA + + z1 = + + z2
γ 2g γ 2g
E1 = E2
With Increase/Decrease in Head:
E1 + hA − hL = E2
 MANILA: Room 206, JPD Building, CM Recto Avenue, Manila
CEBU: 4/F J. Martinez Bldg., Osmeña Blvd., Cebu City
Telephone Number: (02) 516-7559 (Manila) E-Mail: buksmarquez1 @yahoo.com
(032) 254-9967 (Cebu)

EGL = Energy Grade Line = PE + KE - It is the ratio of the actual discharge to the theoretical discharge.
HGL = Hydraulic Grade Line = PE VA
Cv =
VT
SITUATION. Water is issued by a 25 mm diameter nozzle at a rate of 5 m/s. The Coefficient of Velocity, Cv
nozzle is inclined at an angle of 30° with the horizontal. Neglecting air resistance, - It is the ratio of the actual velocity to the theoretical velocity.
determine: VA
16. The vertical distance from highest point to the tip of the nozzle. Cv =
VT
17. The area of the jet at the highest point of the projectile. Coefficient of Contraction, Cc
- It is the ratio of the area of the stream of jet to the area of the opening.
SITUATION. A 50 mm diameter siphon is drawing oil (s = 0.82) from an oil reservoir, C = Cv Cc
as shown in the figure below. If the head loss from point 1 to point 2 is 1.50 m and
from point 2 to point 3 is 2.40 m: ORIFICE – an opening having a closed perimeter in a wall or partition used for
18. Find the discharge of oil from the siphon. measuring flow of fluids.
19. Determine the oil pressure at point 2.
23. The jet from a standard 1.25 cm orifice, in a vertical wall, under a head of
5.50 m, strikes a point 1.50 m horizontally and 12 cm vertically from the jet’s
vena contracta. The discharge is 450 liters in 570 second. Find the three
coefficients of the orifice.

VENTURI METERS – are flow measurement instruments which use a converging

section of pipe to give an increase in the flow velocity and a corresponding pressure
drop from which the flow rate can be deduced.

SITUATION. A 12.5 cm diameter Venturi meter is installed on a pipe 25 cm in

diameter. Determine the discharge that would be passing through the meter when
the double column differential mercury gauge connected to it shows a difference of
20 cm. It is found in a test that the total water passing in the meter is 3500 L for a
period of 45 s.
24. Compute the velocity at the throat.
25. Determine the theoretical discharge.
POWER and EFFICIENCY 26. Determine the meter coefficient.
Power – is the rate at which work is done.
Power = γQH
Efficiency – it is the ratio of the output power to the input power.
Po
E=
Pi

20. Water enters a motor through a 60 cm diameter pipe under a pressure of

14 kPa. It leaves through a 90 cm diameter exhaust pipe with a pressure of
4 kPa. A vertical distance of 2.5 m separates the centers of the two pipes
at the points where the measurements of pressures where taken. If 500
liters of water pass thru the motor, compute the power output of the motor PITOT TUBE – it can be used to measure fluid flow velocity by converting the kinetic
if its efficiency is 80%. energy in a fluid flow to potential energy.

27. A pitot tube with a 90° bend is used to determine the velocity of flow of oil
(SG = 0.82) in a close conduit. The Pitot tube is open at both ends and is
inserted into the flow so that the opening is directed upstream and the other
is directed upwards. The difference between the levels in the pitot tube and
if the fluid surface is 80 mm. What is the velocity of flow?

28. A Pitot tube in a pipe in which air is flowing is connected to a manometer

containing water as in the figure. If the water deflection is 10 cm, what is
the velocity of flow in the pipe, assuming a tube coefficient C P = 0.99.
Specific weight of air is 12 N/m3.
SITUATION. A pump draws water from reservoir A and lifts it to reservoir B as
shown. The loss of head from A to 1 is 3 times the velocity head in the 15 cm pipe
and the loss of head from 2 to B is 20 times the velocity head in the 10 cm pipe. The
discharge in the system is 20 L/s.
21. Compute the power rating of the pump if the efficiency is 85%.
22. Compute the pressure at points 1 and 2.

GATE – is an opening in a dam or other hydraulic structure to control the passage

of water.

SITUATION. For the sluice gate shown, CV = 0.98 and CC = 0.62.

29. What is the flow rate?
30. What is the height of the opening?

FLUID FLOW MEASUREMENTS

Device Coefficients
Coefficient of Discharge, C or Cd