Question

Problem 4 (25 points) A 40 degree inclined water manometer is to measure a gauge pressure of 5000 Pa in a system involving air. The differential length on the manometer is measured with accuracy of 0.5 mm and resolution of 1 mm. Density of air compared to density of water is negligible. Specific weight of water is 9980 +/- 1% N/meter cube. The inclination angle is set to within 0.5 degrees. Calculate the design stage uncertainty in the measurement of this pressure gauge.

Answer 1

The accuracy of chifferential g. Given, Inclination of manometer of 409 Gange pressure, P = 5000 Pa is orn wilt resolution oma 1mm. water, Vwater- = 9980+/-1 allm specific weight of Inclination setup is within 0.5° The Inclined manom ometer would be like, b sino = iz diff. length k مر h = lsimo 40 40 blow mercury lanels. where he vertical height We know that, E: P = 8gh Pressure, Pit Iwater sh Padwater xlsina P HP dwater, sino

= 9950 -1% N/m3 & 0 = 40.0.5° 5000 0. 17141 1980 (hnya 0.76m). 5000 0.719 4 207 m 11950 (6040) f. 719 4207mm de los 719.442.7 m - condition of According given I water max. and min here we are to find going to possible lengths dia 5000 1980 (1-0.01)* Sim (39.5) han l = 0.795598 da a 795.56 mm There is also another possibility le, sweater = 9980 + 14 alma

The resolution of marrionaler 5000 l2 = Uwater & sino 1980 C170.01)x bin 40.5 = 0.763789 & € 763. 79 mm (muide FI l cem cem be, valne :: The maximum of Imax = max (l,,d») + (1,,d 2) + Accuracy 795:56 +0.5 mm e dy+0,5 = 796.06 mm emax 2 The minimum value of e can be &min min (1,, (2) - Accuracy 769.79.0.5 62-0.5 e 763.29 mm lmin is given as Image So, the values of a, lmin, lmax besomes, loin 763777, Imazi 27460 I179 min

The uncertainity in the measurement of the gange is calculated by Pressure remax-1) + (1-2min Uncertainity, 796-779) +(979- 763) t! 2 (17+16 715) = + 16.5 mm ، وارد So, the e could be, l=6197 16.5 mm
​​​Finally,the length(l) including uncertainty is =779+/-16.5 mm