Flow Measurement Worked Examples

A circular sharp-edged orifice has diameter $50.0\text{ mm}$, calibrated discharge coefficient $C_d=0.600$, and center $4.00\text{ m}$ below a large reservoir free surface. Both free surface and jet are at atmospheric pressure. Determine discharge.

An orifice test gives theoretical jet velocity $10.0\text{ m/s}$ and measured vena-contracta velocity $9.50\text{ m/s}$. The vena-contracta area is $60.0\%$ of the geometric orifice area. Determine $C_v$, $C_c$, and $C_d$ using the definitions in this topic.

A water Venturi has $D_1=200\text{ mm}$, $D_2=100\text{ mm}$, measured piezometric-head difference $\Delta h=0.500\text{ m}$ of water, and calibrated $C_d=0.980$. Determine discharge.

A horizontal Venturi carries water. $D_1=300\text{ mm}$, $D_2=150\text{ mm}$, $C_d=0.980$, and a differential mercury manometer connecting equal-elevation taps reads $y=0.120\text{ m}$. Use $SG_{\text{Hg}}=13.6$. Determine discharge.

A $d=100\text{ mm}$ orifice plate is installed in a $D=200\text{ mm}$ water pipe. The compatible pressure-tap measurement gives $\Delta p=20.0\text{ kPa}$ and the calibrated coefficient is $C_d=0.620$. Determine discharge with the incompressible orifice-meter relation.

A calibrated Pitot-static tube in water measures stagnation-minus-static pressure $\Delta p=5.00\text{ kPa}$. Use probe coefficient $C=0.980$ and $\rho=1000\text{ kg/m}^3$. Determine the local velocity.

A free, ventilated suppressed rectangular weir is $L=1.50\text{ m}$ wide with measured head $H=0.300\text{ m}$. Use $C_d=0.620$ in the general rectangular-weir equation. Determine discharge.

A free sharp-crested rectangular weir has physical crest length $L=1.50\text{ m}$, two effective end contractions, and measured head $H=0.200\text{ m}$. Use the stated SI Francis form $Q=1.84(L-0.2H)H^{3/2}$. Determine effective length and discharge.

A free, ventilated $90^\circ$ V-notch has head $H=0.250\text{ m}$ and an applicable coefficient $C_d=0.600$. Determine discharge from the general triangular-weir relation.

A free-flow Cipolletti weir has bottom crest length $L=2.50\text{ m}$. Using the stated SI empirical relation $Q=1.86LH^{3/2}$, determine the head required for $Q=1.00\text{ m}^3/\text{s}$.

A $6.00\text{ m}$ wide channel is divided into five equal $1.20\text{ m}$ subsections. Representative depths are $0.800$, $1.20$, $1.50$, $1.10$, and $0.700\text{ m}$; corresponding representative mean velocities are $0.600$, $0.800$, $1.00$, $0.750$, and $0.500\text{ m/s}$. Estimate discharge with the midsection-style area summation.