University of Nebraska
CIVE 319 – Hydraulics Lab
Instruction Manual
Orifice and Free Jet Flow
Equipment Diagram
Figure 1: Orifice and Free Jet Apparatus
Overview
The rig is designed to be positioned on the side channels of the hydraulics bench top channel.
The inlet pipe should be connected to the bench supply.
An adjustable overflow pipe is provided adjacent to the header tank to allow changes in the head.
A flexible hose attached to the overflow pipe returns excess water to the sump tank. A scale
indicates the water level. Finally a baffle at the base of the tank promotes smooth conditions
prior to the orifice plates.
Two orifice plates of differing diameters are provided and may be interchanged by slackening
the two thumb nuts. The orifice plate is sealed against an 'O'-ring by means of a special fitting
which gives a flush inside surface.
The trajectory of the jet may be plotted using the vertical needles. In operation, a piece of paper
is attached to the backboard, and the needles are adjusted to follow the profile of the water jet.
The needles may be locked using a screw on the mounting bar. The profile may be plotted by
marking the position of the needle top.
A drain plug in the base of the header tank allows water to be drained from the equipment after
use into the channel of the hydraulic bench.
Installation
Locate the apparatus over the molded channel in the top of the bench.
Using the spirit level attached to the base, level the apparatus by adjusting the feet.
Connect the flexible inlet tube on the side of the transparent header tank to the quick release
fitting in the bed of the channel.
Place the free end of the flexible tube from the adjustable overflow on the side of the header tank
in to the volumetric tank (the volumetric tank will not be used for flow measurements). Make
sure that this tube will not interfere with the trajectory of the jet flowing from the orifice.
Position the adjustable overflow tube at mid height and tighten the locknut. Secure each needle
in the raised position by tightening the knurled screw.
Attach the large spring clamp supplied to the top of the back plate. This clamp is used to secure a
sheet of paper when plotting the trajectory of a jet using the needles.
Install one of the two orifices in the fitting at the right hand side of the header tank using the two
securing screws supplied. Ensure that the 'O' ring seal is fitted between the orifice and the tank.
Close the bench flow control valve, switch on the service pump then gradually open the bench
flow control valve. When the water level in the header tank reaches the top of the overflow tube,
adjust the bench flow control valve to give a water level of 2 to 3 mm above the overflow level.
This will ensure a constant head and produce a steady flow through the orifice.
The volume flow rate through the orifice can be determined by intercepting the jet using the
measuring cylinder supplied in conjunction with a stopwatch.
The Orifice and Free Jet Flow apparatus is ready for use.
Technical Data
The following dimensions from the equipment are used in the appropriate calculations. If
required these values may be checked as part of the experimental procedure and replaced with
your own measurements.
Diameter of small orifice
0.003 m
Diameter of large orifice
0.006 m
Surface Area of Reservoir
AR = 1.832 x 10-2 m2
Exercise A
Objective
To determine the coefficient of velocity (CV) and discharge coefficient (Cd) of a small orifice.
Method
By measurement of the trajectory of a jet issuing from an orifice in the side of a reservoir under
steady flow conditions (constant reservoir head).
Equipment Set Up
Position the reservoir across the channel on the top of the hydraulic bench and level the reservoir
by the adjustable feet using a spirit level on the base. Remove the orifice plate by releasing the
two knurled nuts and check the orifice diameter; take care not to lose the O-ring seal. Replace the
orifice and connect the reservoir inflow tube to the bench flow connector. Position the overflow
connecting tube so that it will discharge into the volumetric tank; make sure that this tube will
not interfere with the trajectory of the jet flowing from the orifice.
Turn on the pump and open the bench valve gradually. As the water level rises in the reservoir
towards the top of the overflow tube, adjust the bench valve to give a water level of 2 to 3 mm
above the overflow level. This will ensure a constant head and produce a steady flow through the
orifice.
Theory
From the application of Bernoulli's Equation (conservation of mechanical energy for a steady,
incompressible, frictionless flow):
the ideal orifice outflow velocity at the jet vena contracta (narrowest diameter) is
√
(1)
where h is the height of fluid above the orifice.
Figure 2
The actual velocity is
√
(2)
CV is the coefficient of velocity, which allows for the effects of viscosity and, therefore CV < 1
CV can be determined from the trajectory of the jet using the following argument:
Neglecting the effect of air resistance, the horizontal component of the jet velocity can be
assumed to remain constant so that in time, t, the horizontal distance travelled,
(3)
Because of the action of gravity, the fluid also acquires a downward vertical (Y- direction)
component of velocity. Hence, after the same time, t, (ie. after travelling a distance X) the jet will
have a Y displacement given by
(4)
which can be rearranged to give:
√
(5)
Substitution for t from (5) into (3) and for V from (2) into (3) yields the result:
√
(6)
Hence, for steady flow conditions, ie. constant h, CV can be determined from the X, Y coordinates of the jet. A graph of X plotted against √ will have a slope of 2CV.
The actual flow rate of the jet is defined as:
(7)
where Ac is the cross-sectional area of the vena contracta, given by:
(8)
Where Ao is the orifice area and Co is the coefficient of contraction and, therefore, Cc < 1 Hence
√
(9)
The product CcCV is called the discharge coefficient, Cd , so finally
√
(10)
If Cd is assumed to be constant, then a graph of Qt plotted against √ will be linear and the slope,
√
Procedure
Position the overflow tube to give a high head. Note the value of the head. The jet trajectory is
obtained by using the needles mounted on the vertical backboard to follow the profile of the jet.
Release the securing screw for each needle in turn and move the needle until its point is just
immediately above the jet and re-tighten the screw. Attach a sheet of paper to the back-board
between the needle and board and secure it in place with the clamp provided so that its upper
edge is horizontal. Mark the location of the top of each needle on the paper. Note the horizontal
distance from the plane of the orifice (taken as X = 0) to the co-ordinate point marking the
position of the first needle. This first co-ordinate point should be close enough to the orifice to
treat it as having the value Y = 0. Thus Y displacements are measured relative to this position.
Estimate the likely experimental errors in each of the quantities measured.
Measure the flow rate by timed collection, using the measuring cylinder provided and note the
reservoir head value. Repeat this procedure for different heads by adjusting the level of the
overflow tube.
Plot X vs √ and determine the slope of the graph. The velocity coefficient CV is equal to the
average slope/2.
Plot flow rate Qt vs √ and determine the slope of the graph. The coefficient of discharge Cd can
then be calculated from
√
Head
(m)
X
(m)
1
2
3
4
5
6
7
8
0.0135
0.0635
0.1135
0.1635
0.2135
0.2635
0.3135
0.3635
0.0135
0.0635
0.1135
0.1635
0.2135
0.2635
0.3135
0.3635
Y
(m)
(Yh)0.5
(m)
X
(m)
Y
(m)
(Yh)0.5
(m)
CV
Volume
(m3)
Time
(sec)
Qt
(cms)
h0.5
(m0.5)
Cd