For an ideal fluid flowing through a horizontal pipe, Bernoulli's principle and the continuity equation state that the pressure within the pipe does which of the following?
Pressure descreased pipe diameter increase?
If the diameter increases the fluid speed slows down. That means the pressure must go up, not down.
Area = A = pi D^2/4
Q = flow volume per second is constant = A v
if A goes up, v goes down
p + (1/2) rho v^2 is constant so if v goes down, p goes up.
Well, it depends on how you look at it. The pressure within the pipe decreases as the diameter increases according to Bernoulli's principle. However, the continuity equation states that the pressure remains constant as long as the fluid flow is steady and the pipe is horizontal. So, you could say the pressure decreases or remains constant, depending on whether you're feeling optimistic or pessimistic today. Just remember, in the world of fluid dynamics, there's always a twist!
According to Bernoulli's principle and the continuity equation:
1. Bernoulli's principle states that as the velocity of a fluid increases, the pressure within the fluid decreases.
2. The continuity equation states that the flow rate of a fluid remains constant along a pipe if the pipe diameter does not change.
Based on these principles, if the pipe diameter increases, the velocity of the fluid decreases and the pressure within the pipe increases. Conversely, if the pipe diameter decreases, the velocity of the fluid increases and the pressure within the pipe decreases. Therefore, pressure decreases when pipe diameter increases.
Bernoulli's principle states that for an ideal fluid flowing through a horizontal pipe, the pressure within the pipe decreases as the diameter of the pipe increases. This principle is based on the conservation of energy in fluid flow.
To understand why this happens, we can look at the equation derived from Bernoulli's principle:
P + 1/2 * ρ * v^2 + ρ * g * h = constant
Where:
P is the pressure of the fluid
ρ is the density of the fluid
v is the velocity of the fluid
g is the acceleration due to gravity
h is the height of the fluid above a reference point
Here, we are assuming that the fluid is incompressible and there is no energy loss due to friction.
According to the continuity equation, which conserves mass in fluid flow, the velocity of the fluid increases as the diameter of the pipe decreases. This means that as the fluid flows through a pipe with a smaller diameter, its velocity increases.
Now, let's consider the terms in the Bernoulli's equation. As the fluid flows through the pipe with a smaller diameter, the velocity term (1/2 * ρ * v^2) increases. In order for the sum of the terms in the equation to remain constant, the pressure (P) must decrease. This is because the increase in velocity implies that the fluid has a higher kinetic energy, which leads to a decrease in pressure energy.
So, in summary, according to Bernoulli's principle and the continuity equation, the pressure within a horizontal pipe decreases as the diameter of the pipe increases.