Question

Bernoulli’s equation is applicable to points:
A. In a steadily flowing liquid
B. In a streamline
C. In a straight line perpendicular to a streamline
D. For ideal liquid stream line flow on a streamline

Answer 1

Hint: Total pressure is constant along a streamline assuming flow is incompressible.

Complete step by step solution:
Bernoulli did experiments on liquids hence his equation is applicable only for incompressible fluids.
 We make following assumptions for the Bernoulli equation to be used
the flow must be steady, i.e. the flow parameters (velocity, density, etc...) at any point cannot change with time,
the flow must be incompressible – even though pressure varies, the density must remain constant along a streamline;
Friction by viscous forces must be negligible.
Bernoulli’s equation can be written as
\[{v^2}/2 + gz + p/p = \] constant
v is the fluid flow speed at a point on a streamline,
g is the acceleration due to gravity,
z is the elevation of the point above a reference plane, with the positive z-direction pointing upward – so in the direction opposite to the gravitational acceleration,
p is the pressure at the chosen point, and
ρ is the density of the fluid at all points in the fluid.

Hence, Bernoulli's equation is applicable for ideal liquid stream line flow on a stream line.

Note: Every point in a steadily flowing fluid, regardless of the fluid speed at that point, has its own unique static pressure p and dynamic pressure q. Their sum \[p\; + \;q\] is defined to be the total pressure \[{p_0}\],
static \[pressure + dynamic{\text{ }}pressure = total{\text{ }}pressure\]
\[p + q = {p_0}\]