Question

Po + pgh your objective is to determine the uncertainty of P by measuring Po, p, g and h. Given P Assuming the uncertainty of Po is negligibly small, what is the basic formula for the uncertainty of P? Note Pis not directly measurable, and the only measurable quantities are Po, p. gandh O SP (5Pstat(5Pinstwhere SP stat is the stat ist ical and SPinst is the uncertaint ies of P (5pSgSh) where Sp, 5g, 5h are the uncertainty of p, g and h SP= APPxAPxAPh where APp = Po + (p + 5p)gh,APg = Po + p(g + 5g)h, and AP, = Po + pg(h+5h) O SP= (APp)2 + (APg)2 + (APn where APp = (p 5p)gh, APg = p(g + 5g)h, and AP = pg(h + Sh) SP Sg + Sh where Sp, Sg, Sh are the uncertainty of p, g and h SP Sp SP (Sp)2 + (5g)2 + (Sh)2 where Sp, Sg, Sh are the uncertainty of p, g and h SP (AP)2 (APp)2 (APn) where APp (p + 5p)gh - P, AP, = p(g +5g)h- P, and AP = pg(h+ Sh)- P. +

Answer 1

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