Chapter 7, Problem 7.59P

Interpretation Introduction

(a)

Interpretation:

Using the Bernoulli’s equation, the ethanol discharge velocity and flow rate in L/min should be estimated.

Concept introduction:

Suppose liquid surface in the tank is at point 1 and discharged point is at point 2.

Now, apply Bernoulli equation at point 1 and 2

$\frac{P_1}{\rho g}+\frac{V_1{}^2}{2g}+z_1=\frac{P_2}{\rho g}+\frac{V_2{}^2}{2g}+z_2+h_f$ ……………… (1)

Where

P₁ & P₂ are pressure at section 1 and 2.

V₁ & V₂ are velocity at section 1 and 2.

z₁ & z₂ are the elevation from the horizontal at section 1 and 2.

h_f is the frictional losses

Interpretation Introduction

(b)

Interpretation:

When the discharge is partially closed, the flow rate decreases, which means that $\frac{△u^2}{2}$ changes, however the other term in Bernoulli’s $\frac{△p}{\rho }$ and g?z remains the same. The contradictory result should be explained.

Concept introduction:

Following assumptions are made in the derivation of Bernoulli’s equation:

• The liquid is ideal and incompressible.
• The flow is at steady state and continuous.
• The flow is along the streamline.
• The velocity is uniform over the section and is equal to the mean velocity.
• The only force acting on the fluid are gravity forces and the pressure forces.

Now apply Bernoulli equation at point 1 and 2.

$\frac{P_1}{\rho g}+\frac{V^2{}_1}{2g}+z_1=\frac{P_2}{\rho g}+\frac{V^2{}_2}{2g}+z_2+h_f$