UNIFIED ENGINEERING Fall 2005

Ian A. Waitz

Problem T8 (Unified Thermodynamics)

When a single stream enters a device and a single stream leaves a device, it is typical to apply the steady flow energy equation and balance heat and work against changes in internal energy or changes in enthalpy. Indeed, most of the relationships we have derived focus on changes in these quantities (du=c_vdT, dh=c_pdT, etc.) without reference to the absolute value of these properties.

However, when multiple streams enter or leave a device and these streams mix within the device, it is necessary to know the value of enthalpy and/or the value of internal energy in order to apply the steady flow energy equation. The value is usually calculated relative to a reference value given at a reference temperature as shown below.

and

The specific heats are functions of temperature and are described by polynomials that are experimentally determined (and can be found in the back of most thermodynamics textbooks). However, over small changes in temperature they can be assumed to be constant—as we will do here.

Apply the steady flow energy equation to a device with two inlets and two outlets. Assume the fluid is air, which behaves as an ideal gas with R=287 J/kg-K, c_p=1003.5 J/kg-K, and c_v = 716.5 J/kg-K. The reference enthalpy is 300.47 x10³ J/kg at T_ref = 300 K; the reference internal energy is 214.36 x10³ J/kg at T_ref = 300 K.(MO# 4)

• Inlet 1: mass flow = 13 kg/s, T = 300 K, p = 100x10³ Pa, velocity = 20 m/s
• Inlet 2: mass flow = 2 kg/s, T = 350 K, p = 150x10³ Pa, velocity = 80 m/s
• Outlet 3: mass flow = 7 kg/s, T = 400 K, p = 300x10³ Pa, velocity = 50 m/s
• Outlet 4: mass flow = 8 kg/s, T = 500 K, p = 300x10³ Pa, velocity = 60 m/s
• Heat added to system = 5000 W

a) What is the rate of external (shaft) work done by the device?

b) What is the rate of flow work done by the device?

c) Describe in a sentence or two what flow work is.