Equation of Continuity
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360913 Figure shows a liquid being pushed out of a tube by pressing a piston. The cross-sectional area of the piston is \(1\;c{m^2}\) and that of the tube at the outlet is \(20\;m{m^2}\). If the piston is pushed at a speed of \(1\,cm{s^{ - 1}}\), then the velocity of the outgoing liquid is :
supporting img

1 \(5\,cm{s^{ - 1}}\)
2 \(2.5\,cm{s^{ - 1}}\)
3 \(10\,cm{s^{ - 1}}\)
4 \(7.5\,cm{s^{ - 1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360914 Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is \(3: 2\). Then the ratio of velocities at entry and exit of liquid is

1 \(1: 1\)
2 \(8: 27\)
3 \(9: 4\)
4 \(4: 9\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360915 Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are 3 \(cm\) and 6 \(cm\) respectively. If the speed of water in narrow pipe is \(4\;m/\sec \) and the pressure is \(2.0 \times 10^{4}\) pascal, then the speed of water in the wider pipe is :-

1 \(2\;m/\sec \)
2 \(4\;\,m/\sec \)
3 \(1\,\;m/\sec \)
4 \(3\;\,m/\sec \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360916 Water flows through a horizontal pipe of varying cross-section at a rate of \({0.314 {~m}^{3} {~s}^{-1}}\). The velocity of water at a point where the radius of the pipe is \(10\,cm\) is

1 \({0.1 {~ms}^{-1}}\)
2 \({1 {~ms}^{-1}}\)
3 \({10 {~ms}^{-1}}\)
4 \({100 {~ms}^{-1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360917 Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure). Through a hole of radius \(r\) \((r < < R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x\). Then:
supporting img

1 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{4}}\)
2 \(x=r\left(\dfrac{H}{H+h}\right)\)
3 \(x=r\left(\dfrac{H}{H+h}\right)^{2}\)
4 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{2}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360913 Figure shows a liquid being pushed out of a tube by pressing a piston. The cross-sectional area of the piston is \(1\;c{m^2}\) and that of the tube at the outlet is \(20\;m{m^2}\). If the piston is pushed at a speed of \(1\,cm{s^{ - 1}}\), then the velocity of the outgoing liquid is :
supporting img

1 \(5\,cm{s^{ - 1}}\)
2 \(2.5\,cm{s^{ - 1}}\)
3 \(10\,cm{s^{ - 1}}\)
4 \(7.5\,cm{s^{ - 1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360914 Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is \(3: 2\). Then the ratio of velocities at entry and exit of liquid is

1 \(1: 1\)
2 \(8: 27\)
3 \(9: 4\)
4 \(4: 9\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360915 Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are 3 \(cm\) and 6 \(cm\) respectively. If the speed of water in narrow pipe is \(4\;m/\sec \) and the pressure is \(2.0 \times 10^{4}\) pascal, then the speed of water in the wider pipe is :-

1 \(2\;m/\sec \)
2 \(4\;\,m/\sec \)
3 \(1\,\;m/\sec \)
4 \(3\;\,m/\sec \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360916 Water flows through a horizontal pipe of varying cross-section at a rate of \({0.314 {~m}^{3} {~s}^{-1}}\). The velocity of water at a point where the radius of the pipe is \(10\,cm\) is

1 \({0.1 {~ms}^{-1}}\)
2 \({1 {~ms}^{-1}}\)
3 \({10 {~ms}^{-1}}\)
4 \({100 {~ms}^{-1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360917 Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure). Through a hole of radius \(r\) \((r < < R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x\). Then:
supporting img

1 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{4}}\)
2 \(x=r\left(\dfrac{H}{H+h}\right)\)
3 \(x=r\left(\dfrac{H}{H+h}\right)^{2}\)
4 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{2}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360913 Figure shows a liquid being pushed out of a tube by pressing a piston. The cross-sectional area of the piston is \(1\;c{m^2}\) and that of the tube at the outlet is \(20\;m{m^2}\). If the piston is pushed at a speed of \(1\,cm{s^{ - 1}}\), then the velocity of the outgoing liquid is :
supporting img

1 \(5\,cm{s^{ - 1}}\)
2 \(2.5\,cm{s^{ - 1}}\)
3 \(10\,cm{s^{ - 1}}\)
4 \(7.5\,cm{s^{ - 1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360914 Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is \(3: 2\). Then the ratio of velocities at entry and exit of liquid is

1 \(1: 1\)
2 \(8: 27\)
3 \(9: 4\)
4 \(4: 9\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360915 Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are 3 \(cm\) and 6 \(cm\) respectively. If the speed of water in narrow pipe is \(4\;m/\sec \) and the pressure is \(2.0 \times 10^{4}\) pascal, then the speed of water in the wider pipe is :-

1 \(2\;m/\sec \)
2 \(4\;\,m/\sec \)
3 \(1\,\;m/\sec \)
4 \(3\;\,m/\sec \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360916 Water flows through a horizontal pipe of varying cross-section at a rate of \({0.314 {~m}^{3} {~s}^{-1}}\). The velocity of water at a point where the radius of the pipe is \(10\,cm\) is

1 \({0.1 {~ms}^{-1}}\)
2 \({1 {~ms}^{-1}}\)
3 \({10 {~ms}^{-1}}\)
4 \({100 {~ms}^{-1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360917 Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure). Through a hole of radius \(r\) \((r < < R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x\). Then:
supporting img

1 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{4}}\)
2 \(x=r\left(\dfrac{H}{H+h}\right)\)
3 \(x=r\left(\dfrac{H}{H+h}\right)^{2}\)
4 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{2}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360913 Figure shows a liquid being pushed out of a tube by pressing a piston. The cross-sectional area of the piston is \(1\;c{m^2}\) and that of the tube at the outlet is \(20\;m{m^2}\). If the piston is pushed at a speed of \(1\,cm{s^{ - 1}}\), then the velocity of the outgoing liquid is :
supporting img

1 \(5\,cm{s^{ - 1}}\)
2 \(2.5\,cm{s^{ - 1}}\)
3 \(10\,cm{s^{ - 1}}\)
4 \(7.5\,cm{s^{ - 1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360914 Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is \(3: 2\). Then the ratio of velocities at entry and exit of liquid is

1 \(1: 1\)
2 \(8: 27\)
3 \(9: 4\)
4 \(4: 9\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360915 Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are 3 \(cm\) and 6 \(cm\) respectively. If the speed of water in narrow pipe is \(4\;m/\sec \) and the pressure is \(2.0 \times 10^{4}\) pascal, then the speed of water in the wider pipe is :-

1 \(2\;m/\sec \)
2 \(4\;\,m/\sec \)
3 \(1\,\;m/\sec \)
4 \(3\;\,m/\sec \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360916 Water flows through a horizontal pipe of varying cross-section at a rate of \({0.314 {~m}^{3} {~s}^{-1}}\). The velocity of water at a point where the radius of the pipe is \(10\,cm\) is

1 \({0.1 {~ms}^{-1}}\)
2 \({1 {~ms}^{-1}}\)
3 \({10 {~ms}^{-1}}\)
4 \({100 {~ms}^{-1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360917 Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure). Through a hole of radius \(r\) \((r < < R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x\). Then:
supporting img

1 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{4}}\)
2 \(x=r\left(\dfrac{H}{H+h}\right)\)
3 \(x=r\left(\dfrac{H}{H+h}\right)^{2}\)
4 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{2}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360913 Figure shows a liquid being pushed out of a tube by pressing a piston. The cross-sectional area of the piston is \(1\;c{m^2}\) and that of the tube at the outlet is \(20\;m{m^2}\). If the piston is pushed at a speed of \(1\,cm{s^{ - 1}}\), then the velocity of the outgoing liquid is :
supporting img

1 \(5\,cm{s^{ - 1}}\)
2 \(2.5\,cm{s^{ - 1}}\)
3 \(10\,cm{s^{ - 1}}\)
4 \(7.5\,cm{s^{ - 1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360914 Water is flowing through a tube of non-uniform cross-section. Ratio of the radius at entry and exit end of the pipe is \(3: 2\). Then the ratio of velocities at entry and exit of liquid is

1 \(1: 1\)
2 \(8: 27\)
3 \(9: 4\)
4 \(4: 9\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360915 Water is flowing through two horizontal pipes of different diameters which are connected together. The diameters of the two pipes are 3 \(cm\) and 6 \(cm\) respectively. If the speed of water in narrow pipe is \(4\;m/\sec \) and the pressure is \(2.0 \times 10^{4}\) pascal, then the speed of water in the wider pipe is :-

1 \(2\;m/\sec \)
2 \(4\;\,m/\sec \)
3 \(1\,\;m/\sec \)
4 \(3\;\,m/\sec \)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360916 Water flows through a horizontal pipe of varying cross-section at a rate of \({0.314 {~m}^{3} {~s}^{-1}}\). The velocity of water at a point where the radius of the pipe is \(10\,cm\) is

1 \({0.1 {~ms}^{-1}}\)
2 \({1 {~ms}^{-1}}\)
3 \({10 {~ms}^{-1}}\)
4 \({100 {~ms}^{-1}}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

360917 Consider a water jar of radius \(R\) that has water filled up to height \(H\) and is kept on a stand of height \(h\) (see figure). Through a hole of radius \(r\) \((r < < R)\) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is \(x\). Then:
supporting img

1 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{4}}\)
2 \(x=r\left(\dfrac{H}{H+h}\right)\)
3 \(x=r\left(\dfrac{H}{H+h}\right)^{2}\)
4 \(x=r\left(\dfrac{H}{H+h}\right)^{\frac{1}{2}}\)