unit conversion help

**Tweety** · October 19th 2010, 12:32 PM

I have been given the density of milk = $990 kg m^{-3}$

and a volume of $3000 Litres h^{-1}$ I need to work out the
mass.

I know $\rho\\\\\\\\\\\\( kg m^{-3} ) = \frac{m( kg)}{ v( m^{3})}$

so I need to convert $3000 Litres h^{-1}$ to meters,

can some please check my working.

1L = 1000 ml

1 ml = 1cm

1m = 100cm

$\frac{3000 L}{1 h } \times \frac{1000ml}{1L} = \frac{3000000 ml}{h} = \frac{3000000 cm}{h}$

$\frac{3000000 cm}{h} \times \frac{1m}{100cm} = \frac{30000 m}{h}$

to get m^{3} = $(\frac{30000}{h})^{3} = 2.7 \times 10^{13} m^{3} h^{-1}$

so $m kg = 990 kg m^{-3} \times 2.7 \times 10^{13} m^{3} = 2.673 \times 10^{16} kg$

is this correct ?

**skeeter** · October 19th 2010, 02:14 PM

Originally Posted by Tweety

I have been given the density of milk = $990 kg m^{-3}$

and a volume of $3000 Litres h^{-1}$ I need to work out the
mass.

I know $\rho\\\\\\\\\\\\( kg m^{-3} ) = \frac{m( kg)}{ v( m^{3})}$

so I need to convert $3000 Litres h^{-1}$ to meters,

can some please check my working.

1L = 1000 ml

1 ml = 1cm

1m = 100cm

$\frac{3000 L}{1 h } \times \frac{1000ml}{1L} = \frac{3000000 ml}{h} = \frac{3000000 cm}{h}$

$\frac{3000000 cm}{h} \times \frac{1m}{100cm} = \frac{30000 m}{h}$

to get m^{3} = $(\frac{30000}{h})^{3} = 2.7 \times 10^{13} m^{3} h^{-1}$

so $m kg = 990 kg m^{-3} \times 2.7 \times 10^{13} m^{3} = 2.673 \times 10^{16} kg$

is this correct ?

what do you mean by $Litres h^{-1}$ ?

litres by itself is volume ... $1 \, L = 10^3 \, cm^3 = 10^{-3} \, m^3$

so ... $3000 \, L = 3000 \cdot 10^{-3} \, m^3 = 3 \, m^3$

$m = \rho \cdot V$

$m = 990 \, \frac{kg}{m^3} \cdot 3 \, m^3 = 2970 \, kg$

**Tweety** · October 19th 2010, 02:19 PM

Originally Posted by skeeter

what do you mean by $Litres h^{-1}$ ?

litres by itself is volume ... $1 \, L = 10^3 \, cm^3 = 10^{-3} \, m^3$

so ... $3000 \, L = 3000 \cdot 10^{-3} \, m^3 = 3 \, m^3$

$m = \rho \cdot V$

$m = 990 \, \frac{kg}{m^3} \cdot 3 \, m^3 = 2970 \, kg$

Litres per hour

$\frac{3000 L}{h}$

thanks

**HallsofIvy** · October 20th 2010, 03:02 AM

Then it is not volume, it is a rate of flow.

**Tweety** · October 20th 2010, 06:26 AM

Originally Posted by HallsofIvy

Then it is not volume, it is a rate of flow.

But I can still use it to work out the mass?

**skeeter** · October 20th 2010, 10:22 AM

Originally Posted by Tweety

But I can still use it to work out the mass?

... you get kg/hr

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