Question

A water intake at a pump storage reservoir (the figure) has a cross-sectional area of 0.866 m2. The water flows in at a speed of 0.356 m/s. At the generator building, at distance D = 162 m below the intake point, the cross-sectional area is smaller than at the intake and the water flows out at 8.57 m/s. What is the difference in pressure between inlet and outlet?

Answer 1

Use Bernoulli's principle to solve this problem.

Assume the fluid (water) has frictionless and incompressible flow.

So, we have -

(1/2)∙v² + g∙h + p/ρ = constant

=> (1/2)∙v_i² + g∙h_i + p_i/ρ = (1/2)∙v_o² + g∙h_o + p_o/ρ

(Here, _i denotes inlet _o outlet)

then,

(p_i - p_o) = ρ∙( (1/2)∙(v_o² - v_i²) + g∙(h_o - h_i) )

with D = h_i - h_o

(p_i - p_o) = ρ∙( (1/2)∙(v_o² - v_i²) - g∙D )

put the values of the variables -

(p_i - p_o) = 1000kg/m³∙( (1/2)∙((8.57m/s)² - (0.356m/s)²) - 9.81m/s²∙162m )

= 1000 * (36.66 - 1589.22)

= 1000 * (-1552.56)

= - 1552.56 x 10^3 Pa

= -1552.56 kPa

Therefore, the difference in pressure between inlet and outlet = -1552.66 kPa (Answer)