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Density behind oblique shock for given upstream density and normal upstream Mach number Solution

STEP 0: Pre-Calculation Summary
Formula Used
density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))
ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2))))
This formula uses 3 Variables
Variables Used
Density ahead of shock - Density ahead of shock is the density of the fluid in the upstream direction of shock. (Measured in Kilogram per Meter³)
Specific heat ratio- The Specific heat ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume.
Component of upstream mach normal to oblique shock- Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave
STEP 1: Convert Input(s) to Base Unit
Density ahead of shock: 1 Kilogram per Meter³ --> 1 Kilogram per Meter³ No Conversion Required
Specific heat ratio: 1.392758 --> No Conversion Required
Component of upstream mach normal to oblique shock: 2 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2)))) --> 1*((1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2))))
Evaluating ... ...
ρ 2 = 2.6801865679165
STEP 3: Convert Result to Output's Unit
2.6801865679165 Kilogram per Meter³ --> No Conversion Required
FINAL ANSWER
2.6801865679165 Kilogram per Meter³ <-- Density behind shock
(Calculation completed in 00.005 seconds)

10+ Oblique Shock and Expansion Waves Calculators

Temperature behind oblique shock for given upstream temperature and normal upstream Mach number
temp_behind_shock = Temperature ahead of shock*((1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))) Go
Temperature ratio across the oblique shock
temperature_ratio_across_shock = (1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))) Go
Pressure behind expansion fan
pressure_behind_expansion_fan = Pressure ahead expansion fan*((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1)) Go
Component of downstream Mach number normal to oblique shock for given normal upstream Mach number
component_of_downstream_mach_normal_to_obliqueshock = sqrt((1+0.5*((Specific heat ratio-1)*Component of upstream mach normal to oblique shock^2))/(Specific heat ratio*Component of upstream mach normal to oblique shock^2-0.5*(Specific heat ratio-1))) Go
Pressure ratio across the expansion fan
pressure_ratio_across_expansion_fan = ((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1)) Go
Density behind oblique shock for given upstream density and normal upstream Mach number
density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))) Go
Density ratio across the oblique shock
density_ratio_across_shock = (Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))) Go
Pressure behind oblique shock for given upstream pressure and normal upstream Mach number
static_pressure_behind_shock = Static pressure ahead of shock*(1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1)) Go
Temperature ratio across the expansion fan
temp_ratio_across_expansion_fan = (1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)) Go
Pressure ratio across the oblique shock
pressure_ratio_across_shock = 1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1) Go

Density behind oblique shock for given upstream density and normal upstream Mach number Formula

density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))
ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2))))

Which parameters govern the changes of flow properties across oblique shock?

Oblique shock wave properties in a calorically perfect gas depend only on the normal component of upstream Mach no and which in turn is a function of upstream Mach no. and wave angle. In contrast, the changes in flow properties across normal shock depend on upstream Mach no only.

How to Calculate Density behind oblique shock for given upstream density and normal upstream Mach number?

Density behind oblique shock for given upstream density and normal upstream Mach number calculator uses density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))) to calculate the Density behind shock, The Density behind oblique shock for given upstream density and normal upstream Mach number formula is obtained by multiplying density ratio across the oblique shock to the density ahead of the oblique shock. Density behind shock and is denoted by ρ 2 symbol.

How to calculate Density behind oblique shock for given upstream density and normal upstream Mach number using this online calculator? To use this online calculator for Density behind oblique shock for given upstream density and normal upstream Mach number, enter Density ahead of shock 1), Specific heat ratio (κ) and Component of upstream mach normal to oblique shock (Mn1) and hit the calculate button. Here is how the Density behind oblique shock for given upstream density and normal upstream Mach number calculation can be explained with given input values -> 2.680187 = 1*((1.392758+1)*(2^2)/(2+((1.392758-1)*(2^2)))).

FAQ

What is Density behind oblique shock for given upstream density and normal upstream Mach number?
The Density behind oblique shock for given upstream density and normal upstream Mach number formula is obtained by multiplying density ratio across the oblique shock to the density ahead of the oblique shock and is represented as ρ 2 = ρ 1*((κ+1)*(Mn1^2)/(2+((κ-1)*(Mn1^2)))) or density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))). Density ahead of shock is the density of the fluid in the upstream direction of shock, The Specific heat ratio is the ratio of the heat capacity at constant pressure to heat capacity at constant volume and Component of upstream mach normal to oblique shock is that component of upstream Mach number which is normal to oblique shockwave.
How to calculate Density behind oblique shock for given upstream density and normal upstream Mach number?
The Density behind oblique shock for given upstream density and normal upstream Mach number formula is obtained by multiplying density ratio across the oblique shock to the density ahead of the oblique shock is calculated using density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))). To calculate Density behind oblique shock for given upstream density and normal upstream Mach number, you need Density ahead of shock 1), Specific heat ratio (κ) and Component of upstream mach normal to oblique shock (Mn1). With our tool, you need to enter the respective value for Density ahead of shock, Specific heat ratio and Component of upstream mach normal to oblique shock and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Density behind shock?
In this formula, Density behind shock uses Density ahead of shock, Specific heat ratio and Component of upstream mach normal to oblique shock. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • density_ratio_across_shock = (Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))
  • component_of_downstream_mach_normal_to_obliqueshock = sqrt((1+0.5*((Specific heat ratio-1)*Component of upstream mach normal to oblique shock^2))/(Specific heat ratio*Component of upstream mach normal to oblique shock^2-0.5*(Specific heat ratio-1)))
  • density_behind_shock = Density ahead of shock*((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))
  • static_pressure_behind_shock = Static pressure ahead of shock*(1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))
  • temp_behind_shock = Temperature ahead of shock*((1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2)))))
  • pressure_ratio_across_shock = 1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1)
  • temperature_ratio_across_shock = (1+((2*Specific heat ratio)/(Specific heat ratio+1))*((Component of upstream mach normal to oblique shock^2)-1))/((Specific heat ratio+1)*(Component of upstream mach normal to oblique shock^2)/(2+((Specific heat ratio-1)*(Component of upstream mach normal to oblique shock^2))))
  • pressure_ratio_across_expansion_fan = ((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1))
  • temp_ratio_across_expansion_fan = (1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2))
  • pressure_behind_expansion_fan = Pressure ahead expansion fan*((1+0.5*(Specific heat ratio-1)*(Mach no. ahead expansion fan^2))/(1+0.5*(Specific heat ratio-1)*(Mach no. behind expansion fan^2)))^((Specific heat ratio)/(Specific heat ratio-1))
Where is the Density behind oblique shock for given upstream density and normal upstream Mach number calculator used?
Among many, Density behind oblique shock for given upstream density and normal upstream Mach number calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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