What is Bernoulli’s equation for an ideal fluid flowing between 2 sections of pipewith differing elevation, cross-sectional area and pressures?

A process fluid with a constant density, p kg/m³, enters a vertical cylindrical tank through an inlet pipe at its top. The tank is Dm in diameter and 2.4 m tall. The fluid leaves the tank at the flat bottom through an outlet pipe with an internal diameter dm. When operated at a steady state with 1.2 m liquid level inside the tank, the outlet velocity of the fluid through the bottom pipe, v(t) m/s, can be estimated from Bernoulli equation as:v(t) = 4h(t)where h(t) m is the liquid level inside the tank.(a) Obtain the transfer function between the liquid level inside the tank and the inlet volumetric flow rate when the tank is half full of the liquid.(b) Determine how long it will take for the liquid level inside the tank to increase by 0.1 m when the inlet volumetric flow rate is suddenly increased by 0.01 m³/s from the steady state value. Data: p = 1000 kg/m³, D = 1 m and d = 0.1 m.

Identify the assumptions made for the Bernoulli equation applicable in fluid mechanics. (Check all that apply.)Group of answer choicesAlong a streamlineSteady flowIncompressible flowConstant velocity

The Bernoulli approximation is typically useful in flow regions ______.Group of answer choicesoutside the boundary layersof viscous flowin the boundary layersdirectly downstream of bodies

Water is pumped through an inclined pipe. The pressure, velocity, and datum at the pipe inlet are 10 bar, 17 m/s, and 0 m, respectively. The pressure, velocity, and datum at the pipe outlet are 5 bar, 21 m/s, and 4 m, respectively. Assuming g=10 m/s2 for convenience, determine the change in the Bernoulli head in m for this section of the pipe. The kinetic energy correction factors may be approximated as 1.0 for simplicity.

Water is entering at pressure 4 × 104 pascal with a velocity of 2m/s in a horizontal pipe with cross-sectional area decreasing from 2 × 10–2 m2 to 0.01 m2 . The pressure at smaller cross-section of pipe  in pascal will be :-323.43.4 × 1043.4 × 105