Question

CEIE 240 - Hydraulics Lab #3 Lab Report Due: One week after the lab Bernoulli Theorem Purpose: The purpose of this lab is to verify the Bernoulli conservation of energy relationship. Approach: Conduct an experiment to demonstrate the Bernoulli equation. A schematic of the equipment is shown below. The following data should be collected: TRIAL 1 TRIAL 2 Volume [L] Time (sec) Water Temperature [*C) Port Pipe Diameter (mm) 25 Piezometer Piezometer reading reading (mm) [mm] 13.9 11.8 10.7 (a) Determine the total head (pressure head + velocity head) at each port for each trial. (b) If the total head is not the same across the system for each trial, comment on possible sources of error. Which port had the greatest decrease in pressure head and why? (C) What is the relationship between pressure and velocity in the system? (d) What effect does a higher flowrate have on the system?

Answer 1

Let us get through the calculations first. Please look in the pictures uploaded for calculations and try to understand them.

Given 032 2 3 4 5 Trial a volume Time laug) 56.97sec temp 60.35Sec. Pipedia 19 Piezo Heating (mm) Plezo Readin (rom? (mm Amm 138 139 1118 114 249 g 2 228 69 lo 137 2 225 6x10 -3 m3 Discharge for trald (@1) = Volume - a Time Safset - 91=106 x 10 4 m3/sec Discharge for frial 2 (02) -- 7810- 116xlo- 60.35 sec . ms/ Pressure Head (h) = P, Veloaty Head = 42

L Trial L Post Dia/mm) DELTA PONS Arealm2) Velo Velo Head (m 250 cm Press. Head (1) (WM) 13.9 L 11.8 Timoleo D 4.90x1o 4 1.216 1.518104 701 1,09810-4 8.99x105 7.85 Mors 12350 490%-4 1. 216 2-3711 25mm 4.0.15mm Tomm 0.972 994 273 949 228 1 10.4. g2mm. 25 2.375mm Port I A B C D 1 E IF Sum of Pressure 297.377 298 tvelo. Head (mm) (mm) I mmm 297.15298 (mm) lomm 289 228.327 mm 1 mm.

Dischanse (O2) = 1118x10 m/sec Triala ofta puno Port Pla Area velo Nelo Head : Press Head Total Head (ms) - 12/29 fm) A 25mm 40x1080.236 2,638 1138 140.838 B 13.9 Listo-7.268 30mm 114 luy- c 11.8 1109x1070 842 45.28mm 92 137.22 D (0.7 899 x 10129 84 8(mm 69 153.81 & to 2.85 X10 H 141118mm 26. 137.18 E 254.90x1t 0.236 2.938mm 65 (7.838 my

NOW,

ANS PARB (B) So, as evident, the total head is not constant throughout the trial observations. This can mainly be attributed to 2 factors

firstly, faulty observations - which is always probable but have little significance as the deviations of data are very small.

secondly, due to friction and roughness of the surface. Also, eddies are generated at inlet and exits. However, they are considered marginal due to small length and small flow but are instrumental in causing deviations.

Also, the greatest decrease in pressure is at Port E because at that location the cross-section area is minimum which means that the velocity at that location is highest and therefore, velocity head is also more. But from Bernoulli's equation, we know that total energy remains constant, therefore. Pressure Head decreases at that location to compensate for the increase in the velocity head.

Ans (C) As earlier stated, Bernoullis Conservation of Energy equation states total energy remains constant. Since the vessel is horizontal only pressure and velocity can differ in the system. While one increase other has to decrease to keep the energy conserved.

Ans (d) A higher flow rate will increase the total energy of the system and thus velocity and pressure head both will see a rise. However, the losses are also a function of velocity and discharge, they will also increase in the system.

See, I have tried to be as clear as possible and tried my best to help you here. Hope, this solution works for you, Thank you for reading. DONT FORGET TO UPVOTE IF YOU LIKE THE EXPLANATION.