LAB 3 example maae 2300.pdf - Experiment 3 Flow under a...

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Experiment 3: Flow under a Sluice Gate Summary
The use of the sluice gate allowed us to use mechanical energy in the form of head and calculated velocity to test the validity of Bernoulli’s equation in the case of a hydraulic jump. It was observed and calculated that the hydraulic jump caused inconsistencies within the Bernoulli assumptions. In the case of a sluice gate, the large surface area presents a substantial surface for losses due to friction, this coupled with the turbulence added by the hydraulic jump leads to some interesting results regarding momentum and energy conservation (or lack thereof). Nomenclature P atm = Atmospheric Pressure, usually in Pascals : 101325 Pa [Supplied in Lab] ρ air = Density of Air in kg/m 3 : 1.2kg/m 3 [1] ρ water = Density of Water in kg/m 3 : 1000 kg/m 3 [2] Q= Volume Flow Rate, in m 3 /s z1 = depth of water upstream of Sluice Gate (m) z2 =depth of water downstream of sluice gate (m) z3 = depth of water downstream of hydraulic jump (m) H1 = Flow in head upstream of sluice gate (m) H2= Flow in head downstream of sluice gate(m) H3 = Flow in head downstream of hydraulic jump (m) Zn = Flow of water into v-notch (head) (m) Flow Analysis Section 1 – Bernoulli’s Equation and comparing Velocities Bernoulli’s equation as it is used for this experiment can be assumed to have the same atmospheric pressures as the sluice gate has an open top and thus P 1 and P 2 are equal. (1) 1 2 ρ water v 1 2 + ρ water gh 1 = 1 2 ρ water v 2 2 + ρ water g h 2 (1.1) Rearranging the terms to solve for v 2 and taking into account that v 1 is equal to Q A 1 we get the used equation
V 2 = 2g ( z 2 z 1 ) ( ( A 2 A 1 ) 2 1 ) (1.2) With V 2 calculated V 1 can be found relatively simply, assuming flow rate is constant V 1 = V 2 A 2 A 1 (1.3) To find the experimental velocity we can alter the flow rate equation for the notched tank to: V 2 = 1.38 ( H 2.5 ) W z 2 (2.0) The formula for total head at a particular point in the flow is provided as H tot = P ρg + v 2 2g + z (3.0) The expression for the depth

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