Answered: A 6cm inlet valve and a 3cm exhaust…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A 6cm inlet valve and a 3cm exhaust valve in a turbocharged engine, assume both valves have a discharge coefficient of 0.7 and a lift of 8mm. Find the mass flow rate (in kg/s) at IVO if the cylinder pressure is 115kPa, the inlet manifold pressure is 140kPa, and the manifold air temperature is 310K.

Expert Solution

Step 1

Given,

The diameter of the inlet valve, $D = 6 c m = 6 \times 10^{- 2} m$

The coefficient of discharge, $c_{d} = 0.7$

Lift, $L = 8 m m = 8 \times 10^{- 3} m m$

The cylinder pressure, $p_{1} = 115 k P a = 115 \times 10^{3} P a$

The inlet manifold pressure, $p_{2} = 140 k P a = 140 \times 10^{3} P a$

The manifold air temperature, $T = 310 K$

Step 2

The surface area of the inlet manifold,

$A = πD \times L = π \times 6 \times 10^{- 2} \times 8 \times 10^{- 3} = 1.5 \times 10^{- 3} m m^{2}$

The density of air at $310 K$ is,

$ρ = 1.139 k g / m^{3}$

The velocity at the manifold can be written as,

$∆ p = p_{2} - p_{1} = \frac{1}{2} ρ v^{2} v = \sqrt{\frac{2 ∆ p}{ρ}} = \sqrt{\frac{2 \times (140 \times 10^{3} - 115 \times 10^{3})}{1.139}} = 209.518 m / s$

The mass flow rate at the IVO (Inlet Valve Open) is,

$\dot{m} = c_{d} ρ A v = 0.7 \times 1.139 \times 1.5 \times 10^{- 3} \times 209.518 = 0.25 k g / s$

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