Question

A fluid moves in a steady flow manner between two between two sections
in a flow line. At section 1; 𝐴1= 10𝑓𝑡2
, 𝑣1 = 100 fpm, ѵ = 4 𝑓𝑡3
𝑙𝑏
. At section 2;
𝐴2= 2 𝑓𝑡2
, 𝜌2= 0.20 lb/𝑓𝑡3
. Calculate (a) the mass flow rate and (b) the
speed at section 2.

Answer 1

To solve this problem, we will use the continuity equation and the mass flow equation which states:

Continuity Equation: A1 * v1 = A2 * v2
Mass Flow Equation: m_dot = rho * A * v

(a) Calculate mass flow rate at section 1:
rho1 = 4 ft^3 / lb
m_dot1 = rho1 * A1 * v1

m_dot1 = (4 ft^3 / lb) * (10 ft^2) * (100 fpm)
m_dot1 = 4000 ft^3/min*lb = 4000 lb/min

The mass flow rate is constant along the flow line, so m_dot1 = m_dot2. Therefore, the mass flow rate at section 2 is also 4000 lb/min.

(b) Calculate speed at section 2 using the continuity equation (A1 * v1 = A2 * v2):

A1 = 10 ft^2
v1 = 100 fpm
A2 = 2 ft^2

v2 = (A1 * v1) / A2
v2 = (10 ft^2 * 100 fpm) / 2 ft^2
v2 = 500 fpm

The speed at section 2 is 500 fpm.