Compute the average heat transfer coefficient hc for 10°C water flowing at 4 m/s in a long, 2.5-cm-ID pipe (surface temperature 40°C) by three different equations and compare your results. Also determine the pressure drop per meter length of pipe.

Question

GIVEN

• Water flowing through a pipe

• Water temperature (Tb) = 10°C

• Water velocity (V) = 4 m/s

• Inside diameter of pipe (D) = 2.5 cm = 0.025 m

• Pipe surface temperature (Ts) = 40°C

FIND

(a) The average heat transfer coefficient ( h c) by 3 different equations.

(b) The pressure drop per meter length (?p/L)

ASSUMPTIONS

• Steady state

• Uniform and constant wall surface temperature

• Pipe wall is smooth

• Fully developed flow (L/D > 60)

SKETCH



PROPERTIES AND CONSTANTS

for water at 10°C

for water at 10°C

Density (?) = 999.7 kg/m3

Thermal conductivity (k) = 0.577 W/(m K)

Kinematic viscosity (?) = 1.300 × 10–6 m2/s

Prandtl number (Pr) = 9.5

Absolute viscosity (?b) = 1296 × 10–6 (Ns)/m2

At the surface temperature of 40°C ?s = 658 × 10–6 (Ns)/m2

Answer 1

The Reynolds number for this problem is



(a)

1. Using the Dittus-Boelter correlation



2. Using the Sieder-Tale correlation of



3. Using the Petukhov-Popov correlation of



(b) The friction factor correlation of Equation (7.52) is good only for 1 × 105 < ReD. Therefore, the

friction factor will be estimated from the bottom curve of Figure 7.7: For Re = 7.69 × 104, f ? 0.0188 (Note that this is in good agreement with the friction factor, f in the Petukhov-Popov correlation). The pressure drop per unit length can be calculated