Water at an average temperature of 27°C is flowing through a smooth 5.08-cm-ID pipe at a velocity of 0.91 m/s. If the temperature at the inner surface of the pipe is 49°C, determine (a) the heat transfer coefficient, (b) the rate of heat flow per meter of pipe, (c) the bulk temperature rise per meter, and (d) the pressure drop per meter.

Question

GIVEN

• Water flowing through a smooth pipe

• Average water temperature (Tw) = 27°C

• Pipe inside diameter (D) = 5.08 cm = 0.0508 m

• Water velocity (V) = 0.91 m/s

• Inner surface temperature of pipe (Ts) = 49°C FIND

(a) The heat transfer coefficient ( h c)

(b) The rate of heat flow per meter of pipe (q/L)

(c) The bulk temperature rise per meter of pipe (?Tw/L)

(d) The pressure drop per meter of pipe (?p/L)

ASSUMPTIONS

• Steady state

• Fully developed flow

SKETCH



PROPERTIES AND CONSTANTS

for water at 27°C

Density (?) = 996.5 kg/m3

Specific Heat (cp) = 4178 J/(kg K)

Thermal conductivity (k) = 0.608 W/(m K)

Absolute viscosity (?) = 845.3 × 10–6 (Ns)/m2

Kinematic viscosity (?) = 0.852 × 10–6 m2/s

Prandtl number (Pr) = 5.8 At the surface temperature of 49°C

Absolute viscosity (?s) = 565.1 × 10–6 (Ns)/m2

Answer 1

The Reynolds number for this flow is



Therefore, the flow is turbulent.

The variation in property values is accounted for by using to calculate the Nusselt

number



(b) The rate of convective heat transfer is given by



(c) This rate of heat transfer will lead to a temperature rise in the water given by



(d) From Table 7.4, the friction factor for fully developed turbulent flow through smooth tubes is

given



The pressure drop is given