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>> $Define Incompressible Fluid...$

Define Incompressible Fluid and Identify Examples of Incompressible Fluid Flow

Q: The flow rate of a water from a tap of diameter \$1.25\ cm\$ is \$0.48\ L/min\$. If the coefficient of viscosity of water is \$10^{-3}\ Pa\ s\$, what is the nature of flow of water?

Let the speed of the flow be V.The diameter of the tap = d = 1.25 cm = 1.25 \$\times 10^{-2}\$ m Density of water = \$\rho = 10^3 kg\$ \$ m^{-3}\$viscosity = \$\eta = 10^{-3}\$ Pa sThe volume of the water flowing out per second is Q = \$V \times \frac{\pi d^2}{4}\$ V = \$\frac{4Q}{d^2\pi}\$The Reynolds number is given by R = \$\frac{\rho Vd}{\eta}\$ = \$\frac{4\rho Q}{\pi d \eta}\$ = \$\frac{4 \times 10^3 \times Q}{3.14 \times 1.25 \times 10^{-2} \times 10^{-3}}\$ = \$1.019 \times 10^8 Q\$Hence the flow is turbulent.

Q: Water is flowing continuously from a tap having an internal diameter 8 x 10\$^{-3}\$ m. The water velocity as it leaves the tap is 0.4 m s\$^{-1}\$. The diameter of the water stream at a distance 2 x 10\$^{-1}\$ m below the tap is close to

Given data,\$d_{1}=8\times 10^{-3}m\$\$v_1=0.4ms^{-1}\$\$h=0.2m\$According to equation of motion,\$v_{2}=\sqrt {v{^2_1}+2gh}\$\$=\sqrt{(0.4)^{2}+2\times10\times0.2}\$\$\approx2ms^{-1}\$\$\therefore\$ According to equation of continuity \$a_{1}v_{1}=a_{2}v_{2}\$\$\pi\times\left(\dfrac{8\times10^{-3}}{2}\right)^{2}\times0.4=\pi\times\left(\dfrac{d_{2}}{2}\right)^{2}\times 2\$\$d_{2}=3.6\times10^{-3}m\$

Q: A glass flask of volume \$200 cm^3\$ is just filled with mercury at \$20C\$. The amount of mercury that will overflow when the temperature of the system is raised to \$100C\$ is: \${\gamma _{glass}} = 1.2\times{10^{ - 5}}/{C^ \circ },{\gamma _{mercury}} = 1.8 \times {10^{ - 4}}/{C^ \circ }\$

\$\begin{array}{l}{\gamma _{glass}} = \frac{{\Delta V}}{V}\\ = 1.2 \times {10^{ - 5}}\\\Delta {V_{glass}} = {\beta _{glass}}{V_0}\Delta T\\ = \left( {1.2 \times {{10}^{ - 5}}} \right)\left( {200} \right)\left( {100 - 20} \right)\\ = 0.19c{m^3}\\\Delta {V_{mercury}} = {\beta _{mercury}}{V_0}\Delta T\\ = \left( {1.8 \times {{10}^{ - 5}}} \right)\left( {200} \right)\left( {100 - 20} \right)\\ = 2.9c{m^3}\\\Delta {V_{mercury}} - \Delta {V_{glass}} = 2.9 - 0.19 = 2.7\end{array}\$Hence option (B) is correct.

Q: A fully loaded Boeing aircraft has a mass of \$3.3 \times 10^5\$ kg, its total wing area is \$500 \ m^2\$. It is in level flight with speed of 960 km/h. (a) Estimate the pressure difference between the lower and upper surfaces of the wings. (b) Estimate the fractional increase in the speed of the air on the upper surface of the wing relative to lower surface. (The density of air is \$\rho= 1.2 \ kg \ m^{-3}\$)

(a) the weight of boeing aircraft is balanced by upward force due to the pressure difference.\$\Delta P\times A=3.3\times10^5\times g\$where, \$g=9.8 m/s^2\$\$\Delta P=\dfrac{3.3\times10^5\times9.8}{500}\$\$\Delta P=6.46\times10^3\ N/m^2\$(b) The pressure difference between the lower and upper surface of the wing is \$\Delta P=\dfrac{\rho}{2}(v_2^2-v_1^2)\$\$v_2-v_1=\dfrac{2\Delta P}{\rho(v_2+v_1)}\$\$v_{average}=\dfrac{(v_2+v_1)}{2}=960\ kmph\$or, \$v_{average}=\dfrac{(v_2+v_1)}{2}=266.67\ m/s\$\$v_2-v_1=\dfrac{\Delta P}{\rho\times v_{average}}\$\$\dfrac{v_2-v_1}{v_{average}}=\dfrac{\Delta P}{\rho\times(v_{average})^2}\$\$\dfrac{v_2-v_1}{v_{average}}=\dfrac{6.46\times10^3}{1.2\times(266.67)^2}\$\$\dfrac{v_2-v_1}{v_{average}}=0.075\$

Q: Streamline flow is more likely for liquids with

Streamline flow is more likely for liquids having low density. We know that greater the coefficient of viscosity of a liquid more will be the velocity gradient, hence each of flow can be differentiated streamline flow is related with critical velocity. The critical velocity is that velocity of liquid flow up to which its flow is streamlined and above which its flow becomes turbulent.As critical velocity \$(\eta)\$ and density \$(\rho)\$ of the liquid as \$(V_{c})\propto\dfrac{\eta}{\rho}\$. Hence if the density will be low and viscosity will be high, the value of critical velocity will be more.

Q: A flow of liquid is streamline if the Reynold number is

A flow of liquid is said be a streamline flow if its Reynold number is less than 1000 (or 2000) whereas the flow having Reynold number greater than 4000, is known as turbulent flow.

Q: Differentiate between streamline and turbulent flow.

Laminar Flow- the laminar flow occur in fluid dynamics when a fluid is moving in a small pipe with low speed. 1. The fluid flow in which the layers move in non obstructing manner and the motion is in a straight line. 2. The Reynolds number is less than 2000 in a laminar flow. 3. Shear stress in laminar flow depends only on the viscosity and is independent of the density. Turbulent Flow:-when the fluid move in a pipe of larger diameter and with greater speed then this type of the fluid motion occurs. 1. The layers of the fluid obstruct the motion of the other layer. 2. The Reynolds number is greater than 4000. 3. The shear stress does depends on the density.

Q: The top of a water tank is open to air and its water level is maintained. It is giving out \$0.74 m^3\$ water per minute through a circular opening of 2 cm radius in its wall. The depth of the centre of the opening from the level of water in the tank is close to :

In flow volume = outflow volume\$\Rightarrow \dfrac{0.74}{60} = (\pi \times 4 \times 10^{-4}) \times \sqrt{2 gh}\$\$\Rightarrow \sqrt{2 gh} = \dfrac{74 \times 100}{240 \pi}\$\$\Rightarrow \sqrt{2 gh} = \dfrac{740}{24 \pi}\$\$\Rightarrow 2gh = \dfrac{740 \times 740}{24 \times 24 \times 10} (\pi^2 = 10)\$\$\Rightarrow h = \dfrac{74 \times 74}{2 \times 24 \times 24} \$\$\Rightarrow h \approx 4.8 m\$

Q: Define streamline flow.

Streamline flow (also called flow) is a type of flow of fluid in which fluid in which travels in regular paths. In streamline flow, the velocity, pressure and other such properties remain constant in fluid at each point.

Q: Define turbulent flow.

Turbulent flow is a type of flow of fluid in which the fluid travels in irregular path. In this type of flow, the speed of the fluid at a point undergoes changes continuously in both magnitude and direction. Most kinds of fluid flow are turbulent. Example : flow of air and water.

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Incompressible Fluid and Example of Incompressible Fluid Flow

Incompressible Fluid: The fluid whose density doesn't vary in any sort of flow is considered as incompressible fluid.

Incompressible flow does not imply that the fluid itself is incompressible.
Example of incompressible fluid flow:
The stream of water flowing at high speed from a garden hose pipe. Which tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down. The reason being volume flow rate of fluid remains constant.

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