Fluids

A fluid flows through a pipe with a constant cross-sectional area. If the fluid's velocity increases, what happens to the volume flow rate, assuming the fluid is incompressible?

A pipe's cross-sectional area at point A is $A_1$ and the fluid velocity is $v_1$. At point B, the area is $A_2 = 3A_1$. If the fluid is incompressible, what is the fluid velocity $v_2$ at point B?

An incompressible fluid flows through a pipe. If the diameter of the pipe doubles, what happens to the fluid velocity to maintain the same flow rate?

A fluid flows through a pipe system where both height and area change. At point 1, the pressure is $P_1$, the velocity is $v_1$, and the height is $y_1$. At point 2, the pressure is $P_2$, the velocity is $v_2 = 2v_1$, and the height is $y_2 = 2y_1$. Given that $P_1 = 200 kPa$, $v_1 = 2 m/s$, $y_1 = 1 m$, and the fluid density $rho = 1000 kg/m^3$, find the pressure $P_2$.

Water flows from a large tank through a small hole at the bottom. If the height of the water above the hole is 4.9 meters, what is the exit velocity of the water?

A tank has a hole at a certain depth, and water exits with a velocity calculated using Torricelli's theorem. If the area of the hole is $0.001 m^2$ and the exit velocity is 5 m/s, what is the volume flow rate of the water exiting the tank?

A fluid with a density of $1000 kg/m^3$ flows through a pipe with a radius of 0.05 m at a velocity of 2 m/s. The pipe then narrows to a radius of 0.025 m. What is the mass flow rate in the narrower section?

According to Bernoulli's principle, what happens to the pressure of a fluid as its velocity increases, assuming constant height?

Water flows through a horizontal pipe with varying cross-sectional area. At point 1, the pressure is 200 kPa and the velocity is 2 m/s. At point 2, the velocity is 4 m/s. Assuming the density of water is $1000 kg/m^3$, what is the pressure at point 2?

A large water tank has a small leak near the bottom. The water level is initially at a height $h$ above the hole, and the exit velocity is determined by Torricelli's theorem. If viscous losses are present, how would the actual exit velocity compare to the velocity predicted by Torricelli's theorem?