Streamline Flow — Prelims Questions

Water flows through a horizontal pipe of varying cross-section. At a point where the cross-sectional area is $20,\text{cm}^2$, the water velocity is $1.5,\text{m/s}$. What is the velocity of water at another point where the cross-sectional area is $10,\text{cm}^2$?

A fluid flows through a pipe at a constant height. At a point where the pressure is $P_1$ and velocity is $v_1$, the pipe narrows, and the velocity becomes $v_2$. If $v_2 > v_1$, what can be concluded about the pressure $P_2$ at the narrower section?

Water flows through a vertical pipe. At the lower end, the cross-sectional area is $A_1 = 0.1,\text{m}^2$, and the velocity is $v_1 = 2,\text{m/s}$. The upper end is $5,\text{m}$ above the lower end, and its cross-sectional area is $A_2 = 0.05,\text{m}^2$. Calculate the pressure difference ($P_1 - P_2$) between the lower and upper ends. (Density of water $\rho = 1000,\text{kg/m}^3$, $g = 10,\text{m/s}^2$)

Which of the following conditions is NOT characteristic of streamline flow?

A horizontal pipe has a diameter of $4,\text{cm}$ at one end and $2,\text{cm}$ at the other. Water flows through the pipe. If the pressure difference between the wider and narrower sections is $1500,\text{Pa}$, what is the volume flow rate of water? (Density of water $\rho = 1000,\text{kg/m}^3$)

A fluid has a density of $800,\text{kg/m}^3$ and a dynamic viscosity of $0.0016,\text{Pa\cdot s}$. It flows through a pipe of diameter $0.05,\text{m}$. If the average velocity of the fluid is $0.04,\text{m/s}$, what is the Reynolds number for this flow, and what type of flow is it?

An airplane wing is designed such that the speed of air over its upper surface is $120,\text{m/s}$ and over its lower surface is $90,\text{m/s}$. If the density of air is $1.2,\text{kg/m}^3$, what is the pressure difference between the lower and upper surfaces? (Assume horizontal flow and ideal fluid behavior)