Answer:
will be less than
and
will be greater than
.
Explanation:
The law of conservation of mass states that the rate of fluid mass () entering a system equals the rate at which the fluid mass (
) exits the system.
The mass flow rate can be expressed as follows:
where denotes the fluid density,
signifies the cross-sectional area through which fluid flows, and
represents the fluid's velocity.
Based on the problem conditions, as the fluid's density remains constant, we can write:
where and
are the cross-sectional areas for the fluid flow, while
and
are the corresponding velocities across those areas.
Given the conditions in the problem, , leading from the formula to
.
Furthermore, fluid pressure arises from the fluid's movement through any specific area. When the fluid accelerates, part of its energy increases its speed in the direction of flow, resulting in lower pressure.
Thus, in this instance, the pressure in the larger cross-sectional area
will exceed the pressure
in the smaller cross-sectional area, implying
.