Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version 8th Edition

Published by Wiley
ISBN 10: 1119080703
ISBN 13: 978-1-11908-070-1

Chapter 1 - Problems - Page 32: 1.41

Answer

Calculate the specific gravity of the whipped cream using the following relation: $$ S G=\frac{\rho_{\text {whipped cream }}}{\rho_{\text {water } @ 4^{\circ} C}} $$ Here, the density of water at $4^{\circ} \mathrm{C}$ is $\rho_{\text {water } \mathbb{2} 4^{\circ} \mathrm{C}}$. Substitute $335 \mathrm{~kg} / \mathrm{m}^{3}$ for $\rho_{\text {whippedcream }}$ and $1000 \mathrm{~kg} / \mathrm{m}^{3}$ for $\rho_{\text {water } \mathbb{4} 4^{\circ} \mathrm{C}}$. $$ \begin{aligned} S G &=\frac{335 \mathrm{~kg} / \mathrm{m}^{3}}{1000 \mathrm{~kg} / \mathrm{m}^{3}} \\ &=0.335 \end{aligned} $$ Therefore, the specific gravity $S G$ of the whipped cream is $0.335$.

Work Step by Step

Calculate the mass of the cream using the following relation: $m_{\text {cream }}=\rho V_{\text {cup }}$ Here, the density of cream is $\rho$ and the volume of cup is $V_{\text {cup }}$. Substitute $1005 \mathrm{~kg} / \mathrm{m}^{3}$ for $\rho$. $$ m_{\text {crom }}=\left[1005 \times V_{\text {cup }}\right] \mathrm{kg} $$ Since, the mass of the cream is equal to mass of the whipped cream. $$ \begin{aligned} m_{\text {whipped crom }} &=m_{\text {cream }} \\ &=\left[1005 \times V_{\text {cap }}\right] \mathrm{kg} \end{aligned} $$ Calculate the density of whipped cream using the following relation: $\rho_{\text {whipped croam }}=\frac{m_{\text {whipped cream }}}{3 V_{\text {cup }}}$ Substitute $\left[1005 \times V_{\text {cup }}\right] \mathrm{kg}$ for $m_{\text {whippedcream }} .$ $$ \begin{aligned} \rho_{\text {whippedeream }} &=\frac{\left[1005 \times V_{\text {cup }}\right]}{3 V_{\text {cup }}} \\ &=\frac{1005}{3} \\ &=335 \mathrm{~kg} / \mathrm{m}^{3} \end{aligned} $$ Calculate the specific gravity of the whipped cream using the following relation: $$ S G=\frac{\rho_{\text {whipped cream }}}{\rho_{\text {water } @ 4^{\circ} C}} $$ Here, the density of water at $4^{\circ} \mathrm{C}$ is $\rho_{\text {water } \mathbb{2} 4^{\circ} \mathrm{C}}$. Substitute $335 \mathrm{~kg} / \mathrm{m}^{3}$ for $\rho_{\text {whippedcream }}$ and $1000 \mathrm{~kg} / \mathrm{m}^{3}$ for $\rho_{\text {water } \mathbb{4} 4^{\circ} \mathrm{C}}$. $$ \begin{aligned} S G &=\frac{335 \mathrm{~kg} / \mathrm{m}^{3}}{1000 \mathrm{~kg} / \mathrm{m}^{3}} \\ &=0.335 \end{aligned} $$ Therefore, the specific gravity $S G$ of the whipped cream is $0.335$.
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