### Fuel Flow Rate Calculation**Current Attempt in Progress**A fuel pump sends gasoline from a car's fuel tank to the engine at a rate of \(7.53 \times 10^{-2}\) kg/s. The density of the gasoline is 735 kg/m\(^3\), and the radius of the fuel line is \(2.56 \times 10^{-3}\) m. What is the speed at which gasoline moves through the fuel line?#### Calculation Input- **Mass flow rate (\(\dot{m}\)):** \(7.53 \times 10^{-2}\) kg/s- **Density of gasoline (\(\rho\)):** 735 kg/m\(^3\)- **Radius of the fuel line (r):** \(2.56 \times 10^{-3}\) m#### SolutionTo find the speed at which the gasoline moves through the fuel line, we can use the relationship between mass flow rate, density, and velocity.The formula to use is:\[\dot{m} = \rho \cdot A \cdot v\]Where:- \(\dot{m}\) is the mass flow rate- \(\rho\) is the density of the gasoline- \(A\) is the cross-sectional area of the fuel line- \(v\) is the velocity of gasolineFirst, calculate the cross-sectional area \(A\) of the fuel line:\[A = \pi r^2\]Substitute the given radius:\[A = \pi \times (2.56 \times 10^{-3})^2 \approx 2.06 \times 10^{-5} \, \text{m}^2\]Next, rearrange the original formula to solve for velocity \(v\):\[v = \frac{\dot{m}}{\rho \cdot A}\]Substitute the known values:\[v = \frac{7.53 \times 10^{-2}}{735 \times 2.06 \times 10^{-5}} \approx 5.00 \, \text{m/s}\]#### Final Answer:**Enter the calculated speed of the gasoline through the fuel line:**- **Number:** [Input Box]- **Units:** [Units Drop-down]Please verify the results by substituting the values and

Given formation Mass flow rate of the fuel ( gasoline) (dm/dt) = 7.53 × 10-2 kg/s Density of the…

A fuel pump sends gasoline from a car's fuel tank to the engine at a rate of 7.53x102 kg/s. The density of the gasoline is 735 kg/m, and the radius of the fuel line is 2.56x103 m. What is the speed at which gasoline moves through the fuel line?

A fuel pump sends gasoline from a car's fuel tank to the engine at a rate of 7.53x102 kg/s. The density of the gasoline is 735 kg/m, and the radius of the fuel line is 2.56x103 m. What is the speed at which gasoline moves through the fuel line?

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter15: Fluids

Section: Chapter Questions

Problem 46PQ

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