Problem $3$ Two cylindrical shaped vessels $($LD$-1)$ containing identical mass of water $($density $1000k\frac{g}{m^3}$ and viscosity $0\mathrm{.}001k\frac{g}{m.s}$ and steel and $]=[1000kg$ are to be drained completely within the same duration of time.. If the nozzle dlameter in the vessel containing steel is $40mm,$ determine the corresponding nozzle diameter in the vessel containing water.

Problem $4$: Consider flow of water $($ density $=1000k\frac{g}{m^2})$ through a sudden expansion geometry as shown in the adjoining figure below. Given that mass flow rate is steady and equal to $1\mathrm{.}2k\frac{g}{s}$ and $D_1=4cm$ and $D_2=16cm,$ estimate the drop in pressure between section $1-1$ and $2.2$ on the basis of macroscopic momentum balance consideration.

Problem $5$: $($a$)$ Through a $25$mm diameter nozzle, an inert gas $($argon: density $1\mathrm{.}8\frac{g}{L})$ is blown into liquid steel $($density $7200k\frac{g}{m^3})$ contained in a cylindrical shaped vessel at a rate of $100N\frac{L}{m}in.$ If the depth of liquid in the vessel is $2\mathrm{.}75m$ and the aspect fatio $(\frac{L}{D})=1\mathrm{.}0.$ Estimate the ratlo of potential to kinetic energy input to the system. $($b$)$ The dimensionless mixing time correlation applicable to the above system is $\frac{{}^2\frac{2}{R}2}{R}-K(\frac{Q^2}{g{R}^5}{)}^a(\frac{L}{R}{)}^b.$ Given that ${}_{\text{m}\text{i}\text{x}}{L}^{-1\mathrm{.}0}$ and ${}_{\text{m}\text{i}\text{x}}^{}{Q}^{-0\mathrm{.}33}$ and $K=2980.$ determine the mixing time under the operating conditions mentioned in $($a$).$ consider operating temperature to be $1873K$

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