A horizontal pipe narrows from a diameter of 10 to 5 cm. For an incompressible fluid flowing from the larger diameter to the smaller:
Question 5 options:
1.the velocity and pressure both increase.
2.the velocity increases and the pressure decreases.
3.the velocity decreases and the pressure increases.
4.the velocity and pressure both decrease.
5.the velocity increases but the pressure is unchanged.
The velocity increase and pressure decreases
along a streamline for example down the center Bernoulli equation applies:
p + (1/2) rho v^2 = constant if height does not change
When the diameter decreases, the same amount per second has to flow through a smaller area so velocity increases (continuity)
Therefore
smaller diameter --> faster flow and by Bernoulli thus lower pressure -->2
Velocity increase pressure decreas
8. A horizontal pipe narrows from a diameter of 10 cm to 5cm. For a fluid flowing from the larger diameter to the smaller,
a. the velocity and pressure both increases.
b. the velocity increases and pressure decreases.
c. the velocity decreases and pressure increases.
d. the velocity and pressure both decreases.
Ans is ;b
Yes, option 2 is correct. The velocity increases and the pressure decreases when a fluid flows from a larger diameter to a smaller diameter in a horizontal pipe. This is due to the principle of continuity and Bernoulli's equation. According to continuity, the mass flow rate of the fluid remains constant throughout the pipe. As the area of the pipe decreases, the velocity of the fluid increases to maintain this constant mass flow rate. Bernoulli's equation states that in a horizontal pipe, the pressure is inversely proportional to the velocity. Therefore, as the velocity increases, the pressure decreases.
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Option 2
To determine the relationship between velocity and pressure in a pipe with a narrowing diameter, we can use the principle of conservation of mass and Bernoulli's principle.
According to the principle of conservation of mass, the mass flow rate (m) of an incompressible fluid remains constant in a pipe. This means that the product of the fluid's velocity (v) and cross-sectional area (A) is constant.
Therefore, as the diameter decreases, the cross-sectional area reduces as well. Since the mass flow rate remains constant, the fluid velocity must increase in the narrower section of the pipe to maintain the constant mass flow rate. This eliminates options 3 and 4.
Now let's consider Bernoulli's principle, which states that the total energy of a fluid flowing through a pipe remains constant when there is no energy added or lost. It relates the pressure (P), density (ρ), and velocity (v) of the fluid.
When the diameter of the pipe narrows, the fluid's velocity increases. According to Bernoulli's principle, an increase in fluid velocity is accompanied by a decrease in fluid pressure. This is because the kinetic energy of the fluid increases at the expense of its potential energy (due to pressure).
Therefore, we can conclude that the correct answer is option 2: the velocity increases and the pressure decreases in a horizontal pipe that narrows from a diameter of 10 to 5 cm.