Water is moving with a speed of 5.7 m/s through a pipe with a cross-sectional area of 4.8 cm2. The water gradually descends 9.2 m as the pipe increases to 8.8 cm2. (a) What is the speed at the lower level? (b) If the pressure at the upper level is 1.6 * 105 Pa, what is the pressure at the lower level?

speed of water lower is 3.11 m/s

pressure at the upper level is 261660.95 Pa

Explanation:

Given data

speed = 5.7 m/s

cross-sectional area = 4.8 cm2

water gradually descends = 9.2 m

pipe increases = 8.8 cm2

to find out

speed at the lower level and pressure at the upper level

solution

we will apply here continuity equation i. e

area of pipe top * speed of water top = area of pipe lower * speed of water lower

so speed of water lower = area of pipe top * speed of water top / area of pipe lower

put all value

speed of water lower = 4.8 * 5.7 / 8.8

speed of water lower is 3.11 m/s

in 2nd part we apply bernoulli equation that is

P1 + 1/2 ρ v1² + ρgh1 = P2 + 1/2 ρ v2² + ρgh2

here we know h1 and h2 is initial and final height and ρ is water density

so we calculate p2 here i. e

p2 = P1 + 1/2 ρ (v1² - v2²) + ρg (h1-h2)

put all value we get p2

p2 = 1.6 * 10^5 + 1/2 (1000) (5.7² - 3.11²) + 1000 (9.81) (9.2)

p2 = 261660.95 Pa

pressure at the upper level is 261660.95 Pa