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Bernoulli--Change in Pressure
A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 cm/s in the 2.0-cm section? ( = 1.2 kg/m3.)
A_{1}v_{1}=A_{2}v_{2}=flow-rate
\triangle P=\frac{1}{2}\rho\left(v_{1}^{2}-v_{2}^{2}\right) (I knew how to derive this from Bernoulli's)
flow-rate=A_{1}v_{1}=\frac{1}{4}\pi d_{1}^{2}=\frac{1}{4}\pi\left(0.02m\right)^{2}\left(0.03\frac{m}{s}\right)=9.42\times10^{-6}\frac{m^{3}}{s}
v_{2}=\frac{flow-rate}{A_{2}}=\frac{9.42\times10^{-6}\frac{m^{3}}{s}}{\frac{1}{4}\pi\left(0.01m\right)^{2}}=0.12\frac{m}{s}
\triangle P=\frac{1}{2}\rho\left(v_{1}^{2}-v_{2}^{2}\right)=\frac{1}{2}\left(1.2\frac{kg}{m^{3}}\right)\left[\left(0.03\frac{m}{s}\right)^{2}-\left(0.12\frac{m}{s}\right)^{2}\right]=-8.1\times10^{-3}Pa
All the answers were in Pascals, but somehow my answer was 1,000 times smaller! Since it was multiple-choice, I got the answer right anyways, but I'd like someone to point out where I went wrong. Thanks!
btw, what symbol should I use for the flow rate?
Homework Statement
A venturi tube may be used as the inlet to an automobile carburetor. If the 2.0-cm diameter pipe narrows to a 1.0-cm diameter, what is the pressure drop in the constricted section for an airflow of 3.0 cm/s in the 2.0-cm section? ( = 1.2 kg/m3.)
Homework Equations
A_{1}v_{1}=A_{2}v_{2}=flow-rate
\triangle P=\frac{1}{2}\rho\left(v_{1}^{2}-v_{2}^{2}\right) (I knew how to derive this from Bernoulli's)
The Attempt at a Solution
flow-rate=A_{1}v_{1}=\frac{1}{4}\pi d_{1}^{2}=\frac{1}{4}\pi\left(0.02m\right)^{2}\left(0.03\frac{m}{s}\right)=9.42\times10^{-6}\frac{m^{3}}{s}
v_{2}=\frac{flow-rate}{A_{2}}=\frac{9.42\times10^{-6}\frac{m^{3}}{s}}{\frac{1}{4}\pi\left(0.01m\right)^{2}}=0.12\frac{m}{s}
\triangle P=\frac{1}{2}\rho\left(v_{1}^{2}-v_{2}^{2}\right)=\frac{1}{2}\left(1.2\frac{kg}{m^{3}}\right)\left[\left(0.03\frac{m}{s}\right)^{2}-\left(0.12\frac{m}{s}\right)^{2}\right]=-8.1\times10^{-3}Pa
All the answers were in Pascals, but somehow my answer was 1,000 times smaller! Since it was multiple-choice, I got the answer right anyways, but I'd like someone to point out where I went wrong. Thanks!
btw, what symbol should I use for the flow rate?
