A liquid of density 1.23 × 103 kg/m3 flows steadily through a pipe of varying diameter and height. At location 1 along the pipe the flow speed is 9.23 m/s and the pipe diameter is 1.07 × 101 cm. At location 2 the pipe diameter is 1.71 × 101 cm. At location 1 the pipe is 9.37 m higher than it is at location 2. Ignoring viscosity, calculate the difference between the fluid pressure at location 2 and the fluid pressure at location 1.

To calculate the difference between the fluid pressure at location 2 and the fluid pressure at location 1, we can use the equation of fluid pressure:

𝑃 = 𝜌𝑔ℎ

where:
𝑃 is the fluid pressure,
𝜌 is the density of the liquid,
𝑔 is the acceleration due to gravity, and
ℎ is the height of the fluid column.

First, we need to convert the units to be consistent. The given density is 1.23 × 10^3 kg/m^3, which is already in the correct SI unit. The pipe diameter is given in centimeters, so we need to convert it to meters. Similarly, we need to convert the height from meters to centimeters to be consistent.

1 cm = 0.01 m (conversion factor).

Converting the pipe diameter from cm to m:
diameter_1 = 1.07 × 10^1 cm × 0.01 m/cm = 1.07 × 10^-1 m

Converting the height from m to cm:
height_1 = 9.37 m × 100 cm/m = 937 cm

Next, we can calculate the fluid pressure at location 1 using the given values:

𝑃1 = 𝜌𝑔ℎ1 = (1.23 × 10^3 kg/m^3) × (9.8 m/s^2) × (937 cm × 0.01 m/cm) = 114,654 Pa

Now, let's calculate the fluid pressure at location 2. We are given the pipe diameter at location 2 as 1.71 × 10^1 cm, which needs to be converted to meters:

diameter_2 = 1.71 × 10^1 cm × 0.01 m/cm = 0.171 m

Since the height at location 2 is given as 0 cm (pipe is lower), the term ℎ2 = 0.

𝑃2 = 𝜌𝑔ℎ2 = (1.23 × 10^3 kg/m^3) × (9.8 m/s^2) × (0 cm × 0.01 m/cm) = 0 Pa

Therefore, the difference between the fluid pressure at location 2 and the fluid pressure at location 1 is:

𝑃2 - 𝑃1 = 0 Pa - 114,654 Pa = -114,654 Pa

The difference in pressure is -114,654 Pa. Note that we've ignored viscosity in this calculation.