Viscocity
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361368 Two tubes of radii \(r_{1}\) and \(r_{2}\) and lengths \(l_{1}\) and \(l_{2}\), respectively, are connected in series and a liquid flows through each of them in stream line conditions. \(P_{1}\) and \(P_{2}\) are pressure differences across the two tubes. If \(P_{2}\) is \(4 P_{1}\) and \(l_{2}\) is \(\dfrac{l_{1}}{4}\), then the radius \(r_{2}\) will be equal to -

1 \(4{r_1}\)
2 \({r_1}\)
3 \(2{r_1}\)
4 \(\frac{{{r_1}}}{2}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361369 Two capillaries of same length and radii in the ratio 1: 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is \(2\;m\) of water, the pressure difference across first capillary is

1 \(9.4\;m\)
2 \(1.88\;m\)
3 \(4.9\;m\)
4 \(0.49\;m\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361370 Water is flowing through a capillary tube at the rate of \(20 \times {10^{ - 6}}\;{m^3}/s\). Another tube of same radius and double the length is connected in series to the first tube. Now the rate of flow of water in \(m^{3} s^{-1}\) is

1 \(10 \times 10^{-6}\)
2 \(3.33 \times 10^{-6}\)
3 \(6.67 \times 10^{-6}\)
4 \(20 \times 10^{-6}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361371 Two capillary tubes of the same length but different radii \(r_{1}\) and \(r_{2}\) are fitted in parallel to the bottom of a vessel. The pressure head is \(p\). What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

1 \(r_{1}+r_{2}\)
2 \(\dfrac{r_{1} r_{2}}{r_{1}+r_{2}}\)
3 \(\dfrac{r_{1}+r_{2}}{2}\)
4 None of these
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361372 A volume \(V\) of viscous liquid flows per unit time due to a pressure head \(\Delta P\) along a pipe of diameter \(D\) and length \(L\). Instead of this pipe a set of 4 pipes each of diameter \(\dfrac{D}{2}\) and length \(2 L\) is connected to the same pressure head \(\Delta P\). Now, the volume of the liquid flowing per unit time is

1 \(V\)
2 \(\dfrac{V}{4}\)
3 \(\dfrac{V}{8}\)
4 \(\dfrac{V}{16}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361368 Two tubes of radii \(r_{1}\) and \(r_{2}\) and lengths \(l_{1}\) and \(l_{2}\), respectively, are connected in series and a liquid flows through each of them in stream line conditions. \(P_{1}\) and \(P_{2}\) are pressure differences across the two tubes. If \(P_{2}\) is \(4 P_{1}\) and \(l_{2}\) is \(\dfrac{l_{1}}{4}\), then the radius \(r_{2}\) will be equal to -

1 \(4{r_1}\)
2 \({r_1}\)
3 \(2{r_1}\)
4 \(\frac{{{r_1}}}{2}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361369 Two capillaries of same length and radii in the ratio 1: 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is \(2\;m\) of water, the pressure difference across first capillary is

1 \(9.4\;m\)
2 \(1.88\;m\)
3 \(4.9\;m\)
4 \(0.49\;m\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361370 Water is flowing through a capillary tube at the rate of \(20 \times {10^{ - 6}}\;{m^3}/s\). Another tube of same radius and double the length is connected in series to the first tube. Now the rate of flow of water in \(m^{3} s^{-1}\) is

1 \(10 \times 10^{-6}\)
2 \(3.33 \times 10^{-6}\)
3 \(6.67 \times 10^{-6}\)
4 \(20 \times 10^{-6}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361371 Two capillary tubes of the same length but different radii \(r_{1}\) and \(r_{2}\) are fitted in parallel to the bottom of a vessel. The pressure head is \(p\). What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

1 \(r_{1}+r_{2}\)
2 \(\dfrac{r_{1} r_{2}}{r_{1}+r_{2}}\)
3 \(\dfrac{r_{1}+r_{2}}{2}\)
4 None of these
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361372 A volume \(V\) of viscous liquid flows per unit time due to a pressure head \(\Delta P\) along a pipe of diameter \(D\) and length \(L\). Instead of this pipe a set of 4 pipes each of diameter \(\dfrac{D}{2}\) and length \(2 L\) is connected to the same pressure head \(\Delta P\). Now, the volume of the liquid flowing per unit time is

1 \(V\)
2 \(\dfrac{V}{4}\)
3 \(\dfrac{V}{8}\)
4 \(\dfrac{V}{16}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361368 Two tubes of radii \(r_{1}\) and \(r_{2}\) and lengths \(l_{1}\) and \(l_{2}\), respectively, are connected in series and a liquid flows through each of them in stream line conditions. \(P_{1}\) and \(P_{2}\) are pressure differences across the two tubes. If \(P_{2}\) is \(4 P_{1}\) and \(l_{2}\) is \(\dfrac{l_{1}}{4}\), then the radius \(r_{2}\) will be equal to -

1 \(4{r_1}\)
2 \({r_1}\)
3 \(2{r_1}\)
4 \(\frac{{{r_1}}}{2}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361369 Two capillaries of same length and radii in the ratio 1: 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is \(2\;m\) of water, the pressure difference across first capillary is

1 \(9.4\;m\)
2 \(1.88\;m\)
3 \(4.9\;m\)
4 \(0.49\;m\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361370 Water is flowing through a capillary tube at the rate of \(20 \times {10^{ - 6}}\;{m^3}/s\). Another tube of same radius and double the length is connected in series to the first tube. Now the rate of flow of water in \(m^{3} s^{-1}\) is

1 \(10 \times 10^{-6}\)
2 \(3.33 \times 10^{-6}\)
3 \(6.67 \times 10^{-6}\)
4 \(20 \times 10^{-6}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361371 Two capillary tubes of the same length but different radii \(r_{1}\) and \(r_{2}\) are fitted in parallel to the bottom of a vessel. The pressure head is \(p\). What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

1 \(r_{1}+r_{2}\)
2 \(\dfrac{r_{1} r_{2}}{r_{1}+r_{2}}\)
3 \(\dfrac{r_{1}+r_{2}}{2}\)
4 None of these
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361372 A volume \(V\) of viscous liquid flows per unit time due to a pressure head \(\Delta P\) along a pipe of diameter \(D\) and length \(L\). Instead of this pipe a set of 4 pipes each of diameter \(\dfrac{D}{2}\) and length \(2 L\) is connected to the same pressure head \(\Delta P\). Now, the volume of the liquid flowing per unit time is

1 \(V\)
2 \(\dfrac{V}{4}\)
3 \(\dfrac{V}{8}\)
4 \(\dfrac{V}{16}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361368 Two tubes of radii \(r_{1}\) and \(r_{2}\) and lengths \(l_{1}\) and \(l_{2}\), respectively, are connected in series and a liquid flows through each of them in stream line conditions. \(P_{1}\) and \(P_{2}\) are pressure differences across the two tubes. If \(P_{2}\) is \(4 P_{1}\) and \(l_{2}\) is \(\dfrac{l_{1}}{4}\), then the radius \(r_{2}\) will be equal to -

1 \(4{r_1}\)
2 \({r_1}\)
3 \(2{r_1}\)
4 \(\frac{{{r_1}}}{2}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361369 Two capillaries of same length and radii in the ratio 1: 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is \(2\;m\) of water, the pressure difference across first capillary is

1 \(9.4\;m\)
2 \(1.88\;m\)
3 \(4.9\;m\)
4 \(0.49\;m\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361370 Water is flowing through a capillary tube at the rate of \(20 \times {10^{ - 6}}\;{m^3}/s\). Another tube of same radius and double the length is connected in series to the first tube. Now the rate of flow of water in \(m^{3} s^{-1}\) is

1 \(10 \times 10^{-6}\)
2 \(3.33 \times 10^{-6}\)
3 \(6.67 \times 10^{-6}\)
4 \(20 \times 10^{-6}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361371 Two capillary tubes of the same length but different radii \(r_{1}\) and \(r_{2}\) are fitted in parallel to the bottom of a vessel. The pressure head is \(p\). What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

1 \(r_{1}+r_{2}\)
2 \(\dfrac{r_{1} r_{2}}{r_{1}+r_{2}}\)
3 \(\dfrac{r_{1}+r_{2}}{2}\)
4 None of these
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361372 A volume \(V\) of viscous liquid flows per unit time due to a pressure head \(\Delta P\) along a pipe of diameter \(D\) and length \(L\). Instead of this pipe a set of 4 pipes each of diameter \(\dfrac{D}{2}\) and length \(2 L\) is connected to the same pressure head \(\Delta P\). Now, the volume of the liquid flowing per unit time is

1 \(V\)
2 \(\dfrac{V}{4}\)
3 \(\dfrac{V}{8}\)
4 \(\dfrac{V}{16}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361368 Two tubes of radii \(r_{1}\) and \(r_{2}\) and lengths \(l_{1}\) and \(l_{2}\), respectively, are connected in series and a liquid flows through each of them in stream line conditions. \(P_{1}\) and \(P_{2}\) are pressure differences across the two tubes. If \(P_{2}\) is \(4 P_{1}\) and \(l_{2}\) is \(\dfrac{l_{1}}{4}\), then the radius \(r_{2}\) will be equal to -

1 \(4{r_1}\)
2 \({r_1}\)
3 \(2{r_1}\)
4 \(\frac{{{r_1}}}{2}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361369 Two capillaries of same length and radii in the ratio 1: 2 are connected in series. A liquid flows through them in streamlined condition. If the pressure across the two extreme ends of the combination is \(2\;m\) of water, the pressure difference across first capillary is

1 \(9.4\;m\)
2 \(1.88\;m\)
3 \(4.9\;m\)
4 \(0.49\;m\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361370 Water is flowing through a capillary tube at the rate of \(20 \times {10^{ - 6}}\;{m^3}/s\). Another tube of same radius and double the length is connected in series to the first tube. Now the rate of flow of water in \(m^{3} s^{-1}\) is

1 \(10 \times 10^{-6}\)
2 \(3.33 \times 10^{-6}\)
3 \(6.67 \times 10^{-6}\)
4 \(20 \times 10^{-6}\)
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361371 Two capillary tubes of the same length but different radii \(r_{1}\) and \(r_{2}\) are fitted in parallel to the bottom of a vessel. The pressure head is \(p\). What should be the radius of a single tube that can replace the two tubes so that the rate of flow is same as before

1 \(r_{1}+r_{2}\)
2 \(\dfrac{r_{1} r_{2}}{r_{1}+r_{2}}\)
3 \(\dfrac{r_{1}+r_{2}}{2}\)
4 None of these
PHXI10:MECHANICAL PROPERTIES OF FLUIDS

361372 A volume \(V\) of viscous liquid flows per unit time due to a pressure head \(\Delta P\) along a pipe of diameter \(D\) and length \(L\). Instead of this pipe a set of 4 pipes each of diameter \(\dfrac{D}{2}\) and length \(2 L\) is connected to the same pressure head \(\Delta P\). Now, the volume of the liquid flowing per unit time is

1 \(V\)
2 \(\dfrac{V}{4}\)
3 \(\dfrac{V}{8}\)
4 \(\dfrac{V}{16}\)