**Problem Statement: Mass Flow Rate Calculation**A patient recovering from surgery is being given fluid intravenously. The fluid has a density of 1080 kg/m³, and 6.61 x 10⁻⁴ m³ of it flows into the patient every 8 hours. Find the mass flow rate in kg/s.**Solution:**To find the mass flow rate, we will use the formula:\[ \text{Mass Flow Rate} = \frac{\text{Density} \times \text{Volume Flow Rate}}{\text{Time}} \]Given data:- Density (\( \rho \)): 1080 kg/m³- Volume (\( V \)): 6.61 x 10⁻⁴ m³- Time (\( t \)): 8 hoursFirst, convert the time from hours to seconds:\[ 8 \text{ hours} = 8 \times 3600 \text{ seconds} = 28,800 \text{ seconds} \]Now, calculate the volume flow rate (\( \dot{V} \)):\[ \dot{V} = \frac{V}{t} = \frac{6.61 \times 10⁻⁴ \text{ m³}}{28,800 \text{ s}} \]Calculate the mass flow rate (\( \dot{m} \)):\[ \dot{m} = \rho \times \dot{V} = 1080 \text{ kg/m³} \times \left( \frac{6.61 \times 10⁻⁴ \text{ m³}}{28,800 \text{ s}} \right) \]Perform the calculations:\[ \dot{V} = \frac{6.61 \times 10⁻⁴}{28,800} = 2.294097 \times 10⁻⁸ \text{ m³/s} \]\[ \dot{m} = 1080 \text{ kg/m³} \times 2.294097 \times 10⁻⁸ \text{ m³/s} = 2.478445 \times 10⁻⁵ \text{ kg/s} \]Therefore, the mass flow rate is approximately:\[ 2.48 \times 10⁻⁵ \text{ kg/s} \]

Answered: Image /qna-images/answer/3d6a8194-8e06-45ec-8e9f-39c0a145fa9e.jpg

A patient recovering from surgery is being given fluid intravenously. The fluid has a density of 1080 kg/m³, and 6.61 x 10-4 m³ of it flows into the patient every 8 hours. Find the mass flow rate in kg/s.

A patient recovering from surgery is being given fluid intravenously. The fluid has a density of 1080 kg/m³, and 6.61 x 10-4 m³ of it flows into the patient every 8 hours. Find the mass flow rate in kg/s.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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