The percent error for this flow corresponds to 30.46%, while the error for the
second flow was 33.088%. This percent error was drastically higher than the
percent error associated with the velocity downstream of the sluice gate. The
percent error of V
2
was 3.6% for the first flow and 2.9% for the second flow.
Measuring the first flows velocity it was found to be 2.4221 m/s while calculating its
theoretical value to be 2.5135 m/s; for the second flow the measured velocity was
10 Lab manual

3.0496 m/s and the theoretical was 3.1415 m/s. The volumetric flow rate as well as
the velocity of the two flows was recorded in Table #2 of the Appendix.
The assumptions applied to Bernoulli’s equation as well as the ones applied to the
continuity and momentum equations are not 100% valid and therefore introduce
error into our associated calculations of the Velocity upstream and downstream of
the sluice gate. As a result of the Bernoulli’s equation not taking heat and energy lost
due to friction into account the theoretical velocities are higher than the
experimental velocities
11
. Bernoulli’s equation also implied an incompressible flow
and from the analysis it can be seen that the flow is only incompressible when
operating at supersonic speeds between the sluice gate and hydraulic jump
12
. As
stated above, the measured velocity upstream of the sluice gate had a greater
percent error in its calculations as a result of the V-notch equation not taking into
consideration the velocity of the flow in the reservoir. The velocities found
downstream of the sluice gate minimized the percent error as fewer assumptions
were made and the ones that were applied were valid throughout the system.
The total head loss in the system from the point upstream and downstream of the
sluice gate can be represented by the mechanical energy content lost by the moving
fluid
13
. Theoretically from the flow analysis the two points should contain the same
amount of mechanical energy and therefore have zero head loss. From analyzing the
data in table 1 of the appendix it can be shown that there is mechanical energy lost
by passing under the sluice gate. This loss of mechanical energy can most likely be
attributed to the frictional forces that were assumed to be zero. By moving under the
sluice gate the fluid flow lost energy due to friction between the water and the water
channel/gate
14
.
The knowledge of control volume was applied to the hydraulic jump as well as the
continuity and momentum equations in order to derive an expression, z
3
, for the
theoretical water depth downstream of the hydraulic pump as a function of
upstream depth, z
2
, and flow rate, Q
15
. The equation (17) was found by letting both
1-D flow forces equal one another and rearranging to find z
3
as a function of z
2
. The
quadratic formula was then applied to solve for z
3
. The theoretical depth of the
water downstream of the hydraulic jump was found to be 0.10655 m and measured
11 F.M. White, Fluid Mechanics, 7th Ed., McGraw-Hill, 2010, 257.