The sketch below shows a Venturi meter in action.

$D=$ diameter at meter inlet $=10$ inches

$d=$ diameter at meter throat $=6$ inches

$h1=$ manometer reading at meter inlet $=50+-0\mathrm{.}25$ inches

$h2=$ manometer reading at meter throat $=30+-0\mathrm{.}50$ inches

$Q=$ volumetric flow rate in cfs

The fluid being metered is water at a temperature of $60F.$

Please answer the following question with precision to $3$ decimal places $($i$.$e$.,$ using $4$ significant digits$)$

Part $1.$ What is the theoretical flow coefficient for this meter?

Part $2.$ What is your best estimate for the theoretical volumetric flow rate in cfs$?$

Part $3.$ Establish the actual flow coefficient and its uncertainty using the applicable flow coefficient versus Reynolds number curve on the next page.

Part $4.$ What is your best estimate for the actual volumetric flow rate in cfs$?$

Part $5.$ Use partial derivatives to estimate the upper and lower bounds of the uncertainty for this flow measurement.

FIGURE $13\mathrm{.}13$

Flow coefficient $K$ ane

$R\frac{e_d}{K}$ versus the

Reynolds number for

orifices, nozzles, and

venturi meters. $[$After

Tive $(22)$ and ASME $($

Permission to use Tuvi

granted by

Instrumentation &

Control Systems

magazine, formerly

Instruments magazine.

across the orntice, $h,$ is given as

$\frac{h_L}{h}=\frac{\frac{V_2}{V_1}-1}{\frac{V_2}{V_1}+1}$

Table $13\mathrm{.}1$ shows how the ratio increases with increasing values of $\frac{V_2}{V_1}.$ It is obvious that an orifice is very inefficient from the standpoint of energy conservation.

TABLE $13\mathrm{.}1$ REL$\_$ATIVE HEAD LOSS POR ORIFICES

$\frac{V_2}{V_1},1,2,4,6,8,10$

$\frac{h_L}{}h,0,0\mathrm{.}33,0\mathrm{.}60,0\mathrm{.}71,0\mathrm{.}78,0\mathrm{.}82$