ME 335L Linear Momentum Worksheet
Names: Paul Weaver, Gabe Warren, Taylor Hanson, Nicole Powell
Section #: 3 Group #: 1 Date: 3/24/2022
Relevant Equations:
Relevant Variables:
Area of A Circle:
𝐴 = 𝜋𝑟
𝐴 = Area
𝑟 = Radius
Volumetric Flow Rate:
𝑄 = 𝑣𝐴
𝜌 = Density
𝑄 = Volumetric Flow Rate
Weight:
𝐹 = 𝑚𝑔
𝑣 = Velocity
𝑔 = Gravitational Constant
Mass Flow Rate:
𝑚̇ =
𝜌𝑣𝑑𝐴 ≈∗ 𝜌𝑣𝐴
𝑚 = Mass
𝐹 = External Forces
Conservation of
𝜕
𝜕𝑡
𝑣⃑𝜌𝛿𝑉 +
𝑡 = Time
𝑚̇ = Mass Flow Rate
Linear Momentum:
Conservation of
𝐹=
𝑚̇
𝑣
𝑣⃑𝜌𝑣⃑ ∙ 𝑛 𝑑𝐴 =
−
𝐹 ⃑
𝑚̇ 𝑣
Linear Momentum**:
*In case of average or uniform velocity, constant cross section
**In case of system with steady, incompressible flow with uniform velocity
1.
In your own words, describe the force balance of the system (looking at the jet, not the load cell).
The jet has an initial velocity going up, the forces acting on it are gravity going down and once it hits the plate it
experiences a normal force going down along with horizontal normal forces causing the water to go outwards.
2.
Give an objective of this experiment (what is this experiment trying to show / find).
The objective of this experiment is to show how linear momentum in fluids is conserved by measuring the force it
creates on the plate.
3.
Give a hypothesized outcome of the lab based on what you know about the system and procedure (what do
you expect the results to look like, or how much error do you expect, or do you expect one value to be larger
than another, or how do two things compare).
The hypothesized outcome is that as the flow rate decreases the error will increase because the momentum lost
by gravity will be more prevalent. The transducer will not always even out the force which will create error in the
calculated flow rate.
4.
List all assumptions associated with the process and calculations. Spaces provided do not necessarily align
with answers expected.
Constant room temperature
Incompressible fluid
Constant water density
Motor speed remains constant
Gravity constant
Uniform velocity
5.
List all errors associated with the experiment (try not to include repeats of above). Spaces provided do not
necessarily align with answers expected.
Jet doesn’t reach the plate (20%)
Water could be on top of plate
Water sticks to plate
Gravity affects jet before hitting
Water interferes with itself
Transducer doesn’t cancel out
plate
Human error (Flow rate isn’t exact)
exactly
6.
Choose one of the errors and discuss how it would affect the final results of the experiment. (i.e. what
calculations does it impact, if it has a directional impact would it increase or decrease your answer?)
If the water sticks to the plate instead of spilling over the edge, it causes a small downwards force on the
transducer other than the weight. That would RUIN the equation used for conservation of linear momentum by
adding a term that isn’t accounted for.
7.
Fill out the system conditions and commanded flow rates below.
Temperature:
21.3 C
Pressure:
Nozzle Diameter:
.53in=13.462mm
733.5mmHg
Flow Rates:
100% (Max RPM)
80%
60%
40%
20%
15.054
12.017 GPM
9.027
6.002
3.011
8.
Fill in the following information on the plate:
Weight of Plate:
Initial Force Measured (At
600g
1.33 lbf = 5.92 N
Start):
Calculated Force of Plate
5.886N
Final Force Measured (At End):
% Difference from
0.53
% Change over Runtime:
Expected:
9.
1.31 lbf = 5.83 N
1.50
Capture an image of each flow rate and describe what you are seeing. In your description explain why this
data point is or is not a valid data point.
Flow Rate
100%
Image
Description
This data point is valid because the water is
hitting the plate and fall off the edge
80%
This data point is valid because the water is
hitting the plate and fall off the edge
60%
This data point is valid because the water is
hitting the plate and fall off the edge
40%
This data point is valid because the water is
hitting the plate and fall off the edge
20%
This data point is not valid because the
water is not hitting the plat
10.
In your own words, describe the momentum balance in the non-vertical directions of this system.
By newton’s second law linear momentum is conserved in the system, and the water jet is acting only in the
vertical direction. Therefore, the linear momentum in the horizontal direction must be balanced and equal to 0.
11.
At what flowrate would the plate be floating (the gauge should measure 0)? If possible, command this and
determine what the actual reading at this point is.
F = mv = pQQ/A 14.52GPM (theoretical) 15.027 GPM (actual)