Question

this is from measurement and instruction. looking for solution to understand better .

3.43. in a particular measurement system, quantity x is caicuiated by subtracting a measurement of a quantity : from a measurement of a quantity y, that is, xy- if the possible measurement errors in y and: are tay and b, respectively, show that the value of x can be expressed as-y(ay -bz). (a) What is inconvenient about this expression for x, and what is the basis for the following expression for x that is used more commonly? where e (ay) (bz) (b) In a different measurement system, quantity p is caiculated by muitipiying ments of two quantities q and r such that p qr. if the possibie measurement errors in q and r are tag and br, respectively, show that the value of P can be expressed as P # (qri l tla + b). The volume flow rate of a liquid end of the pipe to discharge into a Figure 3.21). The depth of the liquid in the tank is measured at the start as hi meters and I minute later it is measured as h, meters. if the length and width of the tank are l and the liquid in cubic meters per minute. Calculate the volume flow rate of the liquid if the measured parameters have the following values: in a pipe (the volume flowing in unit time) is measured by allowing the vertical-sided tank with a rectangular base (see w meters, respectively, write down an expression for the volume flow rate of If the possible errors in the measurements of hi, hal, and w are 1,1 , 0.5, and 0.5%. respectively, caiculate the possible error in the calculated value of the flow rate. The volume flow rate of a liquid is caicuiated by ailowing the liquid to flow into a cylindrical tank (stood on its flat end) and measuring the height of the liquicd surface before and after the liquid has flowed for 10 minutes. The voiume collected after 10 minutes is given by Volume = (h2-h1)T(d /2), where h and h2 are the starting and finishing surface heights and d is the measured diameter of the tank. (a) If h 2 m, h2 3 m, and d 2m, calculate the volume flow rate in m'/min. (b) If the possible error in each measurement hi, h2, and d is 1%, determine the likely maximum possible error in the calculated value of volume flow rate (it is assumed that there is negligible error in the time measurement).

Answer 1

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Given h Hew value FoSecomd Cane -
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Alten | Min , dept, tu on) fm e 42x 88 sec in oil 15ea Le.0 巴,021 e7T0 γυ.ord th wi 808 m 1。

tme 13515 lo 15 In gecend care