06. Flow of Fluid
Mechanical Properties of Fluids

143228 A cylindrical vessel of height $50 \mathrm{~cm}$ is filled with water and rests on a table. A small hole is made at the height $h$ from the bottom of the vessel so that the water jet could hit the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.)

1 $15 \mathrm{~cm}$
2 $35 \mathrm{~cm}$
3 $50 \mathrm{~cm}$
4 $40 \mathrm{~cm}$
Mechanical Properties of Fluids

143229 Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as $r=r_{0} \mathrm{e}^{-\alpha x}$, where $\alpha=\frac{1}{3} \mathrm{~m}^{-1}$ and $x$ is the distance from the pipeline inlet. If $R_{1}$ is the Reynold's number for a certain pipeline cross-section at a distance $x_{1}$ metre from the inlet and $R_{2}$ is for distance $\left(x_{1}+3\right)$ metre, then the ratio $\frac{R_{1}}{R_{2}}$ is

1 $\frac{1}{\mathrm{e}}$
2 e
3 $\frac{1}{\mathrm{e}^{3}}$
4 $\frac{1}{\mathrm{e}^{6}}$
Mechanical Properties of Fluids

143230 The average depth of an oil well is $2000\mathrm{~m}$. If the bulk modulus of oil is $8 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and the density of oil is $1500 \mathrm{~kg} / \mathrm{m}^{3}$. The fractional compression at the bottom of the well is (take, $g$ $=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}$ )

1 $3.75 \%$
2 $1.75 \%$
3 $2.75 \%$
4 $4.75 \%$
Mechanical Properties of Fluids

143231 A stream of water flowing horizontally with a speed of $15 \mathrm{~m}-\mathrm{s}^{-1}$ gushes out of a tube of crosssectional area $10^{-2} \mathrm{~m}^{2}$ and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is

1 $2.25 \times 10^{3} \mathrm{~N}$
2 $2.5 \times 10^{3} \mathrm{~N}$
3 $3.0 \times 10^{3} \mathrm{~N}$
4 $3.5 \times 10^{3} \mathrm{~N}$
Mechanical Properties of Fluids

143232 Two capillary of lengths $L$ and $2 L$ and of radii $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X=$ $\frac{\pi \mathrm{pR}^{4}}{8 \eta \mathrm{L}}$ )

1 $\frac{8}{9} \mathrm{X}$
2 $\frac{9}{8} \mathrm{X}$
3 $\frac{5}{7} \mathrm{X}$
4 $\frac{7}{5} \mathrm{X}$
Mechanical Properties of Fluids

143228 A cylindrical vessel of height $50 \mathrm{~cm}$ is filled with water and rests on a table. A small hole is made at the height $h$ from the bottom of the vessel so that the water jet could hit the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.)

1 $15 \mathrm{~cm}$
2 $35 \mathrm{~cm}$
3 $50 \mathrm{~cm}$
4 $40 \mathrm{~cm}$
Mechanical Properties of Fluids

143229 Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as $r=r_{0} \mathrm{e}^{-\alpha x}$, where $\alpha=\frac{1}{3} \mathrm{~m}^{-1}$ and $x$ is the distance from the pipeline inlet. If $R_{1}$ is the Reynold's number for a certain pipeline cross-section at a distance $x_{1}$ metre from the inlet and $R_{2}$ is for distance $\left(x_{1}+3\right)$ metre, then the ratio $\frac{R_{1}}{R_{2}}$ is

1 $\frac{1}{\mathrm{e}}$
2 e
3 $\frac{1}{\mathrm{e}^{3}}$
4 $\frac{1}{\mathrm{e}^{6}}$
Mechanical Properties of Fluids

143230 The average depth of an oil well is $2000\mathrm{~m}$. If the bulk modulus of oil is $8 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and the density of oil is $1500 \mathrm{~kg} / \mathrm{m}^{3}$. The fractional compression at the bottom of the well is (take, $g$ $=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}$ )

1 $3.75 \%$
2 $1.75 \%$
3 $2.75 \%$
4 $4.75 \%$
Mechanical Properties of Fluids

143231 A stream of water flowing horizontally with a speed of $15 \mathrm{~m}-\mathrm{s}^{-1}$ gushes out of a tube of crosssectional area $10^{-2} \mathrm{~m}^{2}$ and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is

1 $2.25 \times 10^{3} \mathrm{~N}$
2 $2.5 \times 10^{3} \mathrm{~N}$
3 $3.0 \times 10^{3} \mathrm{~N}$
4 $3.5 \times 10^{3} \mathrm{~N}$
Mechanical Properties of Fluids

143232 Two capillary of lengths $L$ and $2 L$ and of radii $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X=$ $\frac{\pi \mathrm{pR}^{4}}{8 \eta \mathrm{L}}$ )

1 $\frac{8}{9} \mathrm{X}$
2 $\frac{9}{8} \mathrm{X}$
3 $\frac{5}{7} \mathrm{X}$
4 $\frac{7}{5} \mathrm{X}$
Mechanical Properties of Fluids

143228 A cylindrical vessel of height $50 \mathrm{~cm}$ is filled with water and rests on a table. A small hole is made at the height $h$ from the bottom of the vessel so that the water jet could hit the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.)

1 $15 \mathrm{~cm}$
2 $35 \mathrm{~cm}$
3 $50 \mathrm{~cm}$
4 $40 \mathrm{~cm}$
Mechanical Properties of Fluids

143229 Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as $r=r_{0} \mathrm{e}^{-\alpha x}$, where $\alpha=\frac{1}{3} \mathrm{~m}^{-1}$ and $x$ is the distance from the pipeline inlet. If $R_{1}$ is the Reynold's number for a certain pipeline cross-section at a distance $x_{1}$ metre from the inlet and $R_{2}$ is for distance $\left(x_{1}+3\right)$ metre, then the ratio $\frac{R_{1}}{R_{2}}$ is

1 $\frac{1}{\mathrm{e}}$
2 e
3 $\frac{1}{\mathrm{e}^{3}}$
4 $\frac{1}{\mathrm{e}^{6}}$
Mechanical Properties of Fluids

143230 The average depth of an oil well is $2000\mathrm{~m}$. If the bulk modulus of oil is $8 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and the density of oil is $1500 \mathrm{~kg} / \mathrm{m}^{3}$. The fractional compression at the bottom of the well is (take, $g$ $=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}$ )

1 $3.75 \%$
2 $1.75 \%$
3 $2.75 \%$
4 $4.75 \%$
Mechanical Properties of Fluids

143231 A stream of water flowing horizontally with a speed of $15 \mathrm{~m}-\mathrm{s}^{-1}$ gushes out of a tube of crosssectional area $10^{-2} \mathrm{~m}^{2}$ and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is

1 $2.25 \times 10^{3} \mathrm{~N}$
2 $2.5 \times 10^{3} \mathrm{~N}$
3 $3.0 \times 10^{3} \mathrm{~N}$
4 $3.5 \times 10^{3} \mathrm{~N}$
Mechanical Properties of Fluids

143232 Two capillary of lengths $L$ and $2 L$ and of radii $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X=$ $\frac{\pi \mathrm{pR}^{4}}{8 \eta \mathrm{L}}$ )

1 $\frac{8}{9} \mathrm{X}$
2 $\frac{9}{8} \mathrm{X}$
3 $\frac{5}{7} \mathrm{X}$
4 $\frac{7}{5} \mathrm{X}$
Mechanical Properties of Fluids

143228 A cylindrical vessel of height $50 \mathrm{~cm}$ is filled with water and rests on a table. A small hole is made at the height $h$ from the bottom of the vessel so that the water jet could hit the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.)

1 $15 \mathrm{~cm}$
2 $35 \mathrm{~cm}$
3 $50 \mathrm{~cm}$
4 $40 \mathrm{~cm}$
Mechanical Properties of Fluids

143229 Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as $r=r_{0} \mathrm{e}^{-\alpha x}$, where $\alpha=\frac{1}{3} \mathrm{~m}^{-1}$ and $x$ is the distance from the pipeline inlet. If $R_{1}$ is the Reynold's number for a certain pipeline cross-section at a distance $x_{1}$ metre from the inlet and $R_{2}$ is for distance $\left(x_{1}+3\right)$ metre, then the ratio $\frac{R_{1}}{R_{2}}$ is

1 $\frac{1}{\mathrm{e}}$
2 e
3 $\frac{1}{\mathrm{e}^{3}}$
4 $\frac{1}{\mathrm{e}^{6}}$
Mechanical Properties of Fluids

143230 The average depth of an oil well is $2000\mathrm{~m}$. If the bulk modulus of oil is $8 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and the density of oil is $1500 \mathrm{~kg} / \mathrm{m}^{3}$. The fractional compression at the bottom of the well is (take, $g$ $=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}$ )

1 $3.75 \%$
2 $1.75 \%$
3 $2.75 \%$
4 $4.75 \%$
Mechanical Properties of Fluids

143231 A stream of water flowing horizontally with a speed of $15 \mathrm{~m}-\mathrm{s}^{-1}$ gushes out of a tube of crosssectional area $10^{-2} \mathrm{~m}^{2}$ and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is

1 $2.25 \times 10^{3} \mathrm{~N}$
2 $2.5 \times 10^{3} \mathrm{~N}$
3 $3.0 \times 10^{3} \mathrm{~N}$
4 $3.5 \times 10^{3} \mathrm{~N}$
Mechanical Properties of Fluids

143232 Two capillary of lengths $L$ and $2 L$ and of radii $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X=$ $\frac{\pi \mathrm{pR}^{4}}{8 \eta \mathrm{L}}$ )

1 $\frac{8}{9} \mathrm{X}$
2 $\frac{9}{8} \mathrm{X}$
3 $\frac{5}{7} \mathrm{X}$
4 $\frac{7}{5} \mathrm{X}$
Mechanical Properties of Fluids

143228 A cylindrical vessel of height $50 \mathrm{~cm}$ is filled with water and rests on a table. A small hole is made at the height $h$ from the bottom of the vessel so that the water jet could hit the table surface at a maximum distance $x_{\max }$ from the vessel as shown in the figure. The value of $x_{\max }$ will be (Neglect the viscosity of water.)

1 $15 \mathrm{~cm}$
2 $35 \mathrm{~cm}$
3 $50 \mathrm{~cm}$
4 $40 \mathrm{~cm}$
Mechanical Properties of Fluids

143229 Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as $r=r_{0} \mathrm{e}^{-\alpha x}$, where $\alpha=\frac{1}{3} \mathrm{~m}^{-1}$ and $x$ is the distance from the pipeline inlet. If $R_{1}$ is the Reynold's number for a certain pipeline cross-section at a distance $x_{1}$ metre from the inlet and $R_{2}$ is for distance $\left(x_{1}+3\right)$ metre, then the ratio $\frac{R_{1}}{R_{2}}$ is

1 $\frac{1}{\mathrm{e}}$
2 e
3 $\frac{1}{\mathrm{e}^{3}}$
4 $\frac{1}{\mathrm{e}^{6}}$
Mechanical Properties of Fluids

143230 The average depth of an oil well is $2000\mathrm{~m}$. If the bulk modulus of oil is $8 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$ and the density of oil is $1500 \mathrm{~kg} / \mathrm{m}^{3}$. The fractional compression at the bottom of the well is (take, $g$ $=\mathbf{1 0} \mathbf{~ m} / \mathrm{s}^{2}$ )

1 $3.75 \%$
2 $1.75 \%$
3 $2.75 \%$
4 $4.75 \%$
Mechanical Properties of Fluids

143231 A stream of water flowing horizontally with a speed of $15 \mathrm{~m}-\mathrm{s}^{-1}$ gushes out of a tube of crosssectional area $10^{-2} \mathrm{~m}^{2}$ and hits a vertical wall nearly. The force exerted on the wall by the impact of water assuming it does not rebound is

1 $2.25 \times 10^{3} \mathrm{~N}$
2 $2.5 \times 10^{3} \mathrm{~N}$
3 $3.0 \times 10^{3} \mathrm{~N}$
4 $3.5 \times 10^{3} \mathrm{~N}$
Mechanical Properties of Fluids

143232 Two capillary of lengths $L$ and $2 L$ and of radii $R$ and $2 R$ are connected in series. The net rate of flow of fluid through them will be (given rate of the flow through single capillary, $X=$ $\frac{\pi \mathrm{pR}^{4}}{8 \eta \mathrm{L}}$ )

1 $\frac{8}{9} \mathrm{X}$
2 $\frac{9}{8} \mathrm{X}$
3 $\frac{5}{7} \mathrm{X}$
4 $\frac{7}{5} \mathrm{X}$