CALCULATION OF PRESSURE DROP

Before getting in calculation step, it has to be defined relevant assumptions which can make the calculation easier and the error is tolerable.

The assumptions for the exhaust are:

  • The channel is straight enough in the other hand no sharp turns so minor losses of the turns become zero

  • The roughness of channel surface is uniform

  • The temperature along the channel is uniform with assumption that the exhaust is isolated until no heat come out and in

  • The inner comp in the actual exhaust pipe doesn’t exist

Besides that another important thing is if the outer channel is higher than inner channel, the Δz has positive value and vice versa.



Exhaust Schema, (a) with turn, (b) straight assumption


From figure above, we can see that the diameter of the channel is not constant. In turn side, which can be assumed to be straight, the diameter is uniform, after that the diameter changes linearly. This means pressure drop will different in each diameter changes. While height difference of the channel-in only happens on turn side, after it is zero.

Generally, pressure-out is difference of pressure when exhaust gas exits from engine valves minus amount of pressure drop




Fig. 2 Otto cycle


From figure above, exhaust gas pressure exits from valves at position 4 which can be defined from amount of maximum pressure at dead point at position 3. Until to get pressure at gas exit from engine valves is



where PMax is maximum pressure at compression, rc is compression ratio and k is specific heat ratio.

For standard analysis, we can use air property to get gas exhaust gas. To get the parameter it needs exhaust gas temperature which is



where Tmax is maximum temperature at compression.

We can get gas exhaust parameters that are density (ρ), and kinematics viscosity (υ).

Flow mass of gas exhaust is equal to air plus exhaust gas:



where ρatmosphere is air density at atmosphere condition outside the engine, so average flow rate is defined:



where A is extent of the channel, and we can get Reynold Number:



Flow on the channel can be described with Bernoulli equation:



where z is height between channel-out and channel-in.

Bernoulli equation says that total head in horizontal direction (in this case at x direction) is constant, which means velocity head can be replaced with gravity head or pressure head meaning constant too. In this flow it is assumed no energy loss.

For viscous fluids, mechanical energy changes into heat (in the viscous boundary layer along channel wall) and disappears from the flow. Until we can’t use Bernoulli principle from energy conversion to calculate parameter of the flow. So, we have to use added equation (called viscous head) into Bernoulli equation, and we get



where d is diameter of the channel.

Until the equation above can be integrated into:



where Δz is height between channel-out and channel-in, and L is length of the channel. While f is friction factor, which depends on Reynold Number (Re) from the channel flow and relative roughness e/D of the channel wall,



value of e is defined from surface roughness that depends on the channel material..


Table 1 Surface roughness value according to channel material


For laminar flow (Re<2000), f is defined from this equation:



For turbulence flow (Re>3000), f is defined from this equation:



or from Moody graphic


Fig. 3 Moody Chart



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1 comment:

  1. That really helpful post. It is the same like the injection engine in Motor Matic Injeksi Irit Harga Murah or not?. By the way i have one more information which you might like. It's about promo indonesia held by alfamart minimarket. You must have know about it before right?. It called Promo Member Alfamart Minimarket Lokal Terbaik Indonesia. You should check it out for more information.

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