Final answer:
To find the pressure difference between two locations in a fluid flowing through a pipe, we can use Bernoulli's equation.
Step-by-step explanation:
To find the pressure difference between location 2 and location 1, we can use Bernoulli's equation.
Bernoulli's equation states that the total pressure at two locations in a fluid flowing through a pipe is equal to the sum of the pressure due to the fluid's height and the pressure due to the fluid's velocity.
Using Bernoulli's equation, we can write:
ΔP = P2 - P1 = ρgh2 - ρgh1 + 1/2 ρv1^2 - 1/2 ρv2^2
Where:
- ΔP is the pressure difference between location 2 and location 1
- P2 is the pressure at location 2
- P1 is the pressure at location 1
- ρ is the density of the liquid
- g is the acceleration due to gravity
- h2 is the height of location 2 from a reference point
- h1 is the height of location 1 from the same reference point
- v1 is the flow speed at location 1
- v2 is the flow speed at location 2
Plugging in the given values:
ΔP = (1370 kg/m3) * 9.8 m/s2 * 0 - (1370 kg/m3) * 9.8 m/s2 * 0 + 1/2 * (1370 kg/m3) * (1.47 m/s)2 - 1/2 * (1370 kg/m3) * (v2)2
The pressure difference, ΔP, is equal to the difference in kinetic energy per unit volume between the two locations.
To find the value of ΔP, we need to know the value of v2.