1. FEEG1003 ThermoFluids
Answer:
Introduction
Generally, a fluid is a liquid or a gas. The fluid can always be set in motion under certain
principles of the Bernoulli's. The flow is always assumed to be laminar or streamlined
without eddy effects. The fluid in motion can induce forces on objects that get into touch
with them in a natural or manufactured state. The assumptions that usually guide these
motions are that the flow is non-viscous, the flow is steady, the flow is streamlined or
laminar, and there should only be one exit and one inlet. The basic parameters in fluid flow
are volumetric flow rate, which is the volume passing in a given section per unit second, the
mass flux, which is the mass of the fluid passing in a given area per unit second and lastly
the fluid velocity, which is the rate of flow of the fluid. (McGill & King, 1995). To learn fluid
motion, a finite section of liquid is typically chosen, and the effects of the flow, such as the
force on an object, are calculated by computing the gross mass rate that flows into and out
of control volume (McGill & King, 1995). These forces can be calculated using Newton's
second law (the momentum equation) as in solid mechanics. The momentum equation can
also compute the force impacted by a fluid jet on a curved or a flat surface. Fluid dynamics
and hydraulic designs demands explicit knowledge of such forces. (Sutton, 2001)
Engineers and designers use the momentum equation to quantify a motion or flowing fluid's
force on the solid body. For example, turbines generate power or electricity in hydropower
plants. The turbines rotate because of the exerted force by one or many water jets directed
tangentially against the vanes or the buckets of the turbine. The impact of the water on the
vanes causes a torque on the wheel, which causes the turbine to spin, causing electricity
generation (Kleppner & Kolenkow, 2012). The above designs can also be utilized to
manufacture hydraulic machines and brake systems, thermal power plants, nuclear power
plants, and other various instruments.
The physical operating characteristics of a laboratory-based rocket engine demonstration
are examined in this research. The theoretical performance of the rocket engine is evaluated
and equated to laboratory outcomes collected from experimental conditions. The data that
were obtained were contrasted, and the deviations are noted, examined, and tabulated.
2. Aims And Objectives
This experiment explores certain forces of reaction caused by a fluid flow's change in
momentum when a jet of water contacts a flat plate or a spiral or curved surface and
compares the experimental results to the computed forces using the momentum equation.
The second goal is to calculate a rocket engine's theoretical performance and compare it to
experimental data.
Experimental Procedure
Equipment Description And Setup
The apparatus comprises a clear acrylic cylinder, a nozzle, and a flow deflector. Water goes
in vertically from the top of the cylinder, strikes the target placed on a stem, and exits via
the outlet holes on the base of the cylinder. The air vents maintain the surface pressure
within the cylinder above. To allow masses to counterbalance the striking water force,
the pan is placed above the stem. The jet apparatus is as featured below;
Figure 1: The jet apparatus
Apparatus And Levelling And The Basic Checks
Inspect a transparent acrylic jet nozzle tank to ensure it is appropriately positioned inside
the molded channel placed above the bench. The equipment must be level. Make sure the
bubble level above the plate of the device is in or in the spot or center loop by using the
adjustable feet. This is as illustrated below;
Figure 2: Jet apparatus positioning on bench
Installing Or Replacement Of The Target.
This was accomplished by starting with a 90° deflection angle on the target piece. It was
conducted by removing the three knurled nuts that held the top plate of the transparent
tank in place, followed by carefully removing the top plate. As seen below, screw the flat
target plate onto the vertical shaft's end. It was completed as shown below;
Replace the transparent tank's top plate and ensure the level bubble is in the center of its
circle. If necessary, adjust the feet to re-level the transparent tank. To keep the top plate
level, replace the three knurled nuts and tighten them in order, as shown by the spirit level.
It's important not to overtighten over loosen the knurled nuts because this might harm the
top plate; only tighten them enough to the plate level.
Figure 3: Zeroing of the mass pan
3. Ascertain the spring positioned in the recesses, allowing the movement of the vertical shaft
freely while still being supported by the spring below the mass pan. Ensure the point gauge
level is the same as the mass pan's center mark. Check that the pan returns to the zero
position by pressing down on the spring. This was as illustrated below;
Figure 4: Zeroing of the mass pan
Measurement Procedure
Most negligible masses were added to the mass pan. A bench-controlled valve was fully
turned clockwise (off) and started the pump. The black control valve was opened until the
mass pan was level with the point indicator.
A plug was inserted inside the bench sump, and the water was timed accumulation using a
stopwatch. Use the upper volumetric scale.
The next mass increment was added, and the flow rate increased to level the mass pan. The
water was drained out of the sump up to just below the upper step, reinserted the ball plug,
and the time the water accumulated.
The above steps were repeated for all increments of mass.
A bench was turned off, the masses were removed, and closed the bench flow control valve
was, and they were all done in that order.
Setup steps 2 & 3 were repeated to reset the apparatus for the 120° target. Repeat
measurement procedure steps a) to e).
Setup steps 2 & 3 were repeated to reset the apparatus for the 180° target. Repeat
measurement procedure steps a) to e).
Theoretical Analysis
Newtonian mechanics and linear momentum are usually computed by obtaining the
numerical product of the velocity of an object and its absolute mass. This is always a vector
quantity that exhibits the direction and the magnitude. Momentum generally relies on
Newton's second law of motion, and it is always a conserved quantity. This is always
described best in the conservation of the linear momentum. Initially, the sum of momentum
is at equilibrium with the sum of the momentum after the action of forces in a system. The
fluid mechanics generates the primary basis of hydraulics engineering that relies on the
utilization of the properties of the fluids in many applications, from the dam design to liquid
spray systems.
The water velocity exiting the nozzle with any given cross-sectional area is provided by the
following equation; (Sutton, 2001)
It is revealed that the flow velocity does not vary as the water passes around the deflector;
only the flow direction changes; this is evident when the energy equation is applied
between the nozzle outlet and the deflector's surface. When the momentum equation is
used to a control volume containing the deflected flow, the following conclusions are
obtained: (Sutton, 2001)
4. N/B was used in excel to find theoretical force
Based on the principle of moments and forces of equilibrium that acts in an upright
direction, is stabilized by the weight applied on the weight pan, where m is the applied
mass), i.e., . Therefore:
Results And Discussion
The collected results were as shown below; they are grouped in terms of the degrees of the
target with a constant area of the target in square meters.
The data of velocity and weight were as shown;
The graph of the measured force Versus theoretical force is shown below;
The graph was as shown below;
Conclusion
This experiment explored the forces of reaction caused by a fluid flow's change in
momentum when a jet of water contacts a flat plate or a spiral or curved surface and
compares the experimental results to the computed forces using the momentum equation.
The second goal was to calculate a rocket engine's theoretical performance and compare it
to experimental data. The objective of the experiment was usefully achieved, and the data
obtained from the flow rates were sued to draw or plot the graph of the measured and the
theoretical forces. It emerged that the applied force technically depends on the velocity, the
deflection angle, and the flow rate. All the expectations, as instructed, were carefully
analyzed. The change application in this kind of momentum was examined and found quite
helpful in many engineering designs. It was also noted that the deflection angle could be
adjusted, which can significantly maximize the fluid flow discharge.
References
Kleppner, & Kolenkow. (2012). An Introduction to Mechnaics.
McGill, & King. (1995). Engineering Mechanics, An Introduction to Dynamics. PWS
Publishing Company.
Sutton, G. (2001). Rocket Propulsion Elements(7th ed.). John Wiley & Sons.
