What is the formula for calculating how much sugar sugar syrup contains?

[ugcheleuce]

density(x)=sg(x)*sg(water)
density(water) ~ 1kg/litre

Thanks for clarifying.

So when you say "the weight of sugar per litre of solution is brix*density(brix)" then I assume it means that I can simply take the figure in the "brix" column and multiply it by the figure in the "gravity" column, to get the weight (in kilogram) of sugar in one litre of syrup.

I tested it with values given by beekeepers from actual measurements, and it does seem to work like that, thanks.

 

[user 6228]

Thanks for clarifying.

So when you say "the weight of sugar per litre of solution is brix*density(brix)" then I assume it means that I can simply take the figure in the "brix" column and multiply it by the figure in the "gravity" column, to get the weight (in kilogram) of sugar in one litre of syrup.

I tested it with values given by beekeepers from actual measurements, and it does seem to work like that, thanks.

i ve corrected it to what i thought i wrote
density(x)=sg(x)*density(water)
density(water) ~ 1kg/litre

yes
brix * gravity = kg/l (near enough)

 

[Amari]

Thick 2lb sugar to 1 pint of water gives 61.5% sugar concentration
Thin 1lb sugar to 2 pints of water gives 28% sugar concentration

"Thin', as fed in spring, is surely 1 lb sugar to 1 pint water?

 

[ugcheleuce]

Thin 1 lb sugar to 2 pints of water gives 28% sugar concentration.

"Thin", as fed in spring, is surely 1 lb sugar to 1 pint water?

Both are acceptable.

1 lb sugar + 1 pint water = 44.4% solution
1 lb sugar + 2 pints water = 28.5% solution

In NL the 1:1 solution is a 50% solution (we use kilograms and litres), but spring feeding can be thinner, since the purpose of it isn't to feed sugar but to simulate a nectar flow so that the bees are encouraged to go out -- it can be even thinner, e.g. 1:2 (which in NL would be a 33.3% solution).

 

[ugcheleuce]

density(x)=sg(x)*density(water)
density(water) ~ 1kg/litre
yes
brix * gravity = kg/l (near enough)

Okay, here's the next conundrum. I have jerry cans with sugar and syrup (some of the sugar didn't dissolve, so it lies packed tightly at the bottom of the jerry can). I carefully pour off the syrup so that the syrup I pour off doesn't contain undissolved granules of sugar. I then weigh/measure the poured-off syrup to determine what percentage the solution is. The syrup is quite thick, so I imagine it will be 3:2 or 2:1 at least.

Now... 2 litres of syrup weighs 2.4 kg.
Then, what is the percentage of sugar in the syrup?

Maths is not my strong point, but my logic says that the water in the syrup weighs 1 kg per litre, so if I can deduct the water weight, I'll be left with the sugar weight.

2 litres of syrup = 2.4 kg
i.e. 1 litre of syrup = 1.2 kg
1 litre of syrup = 1 kg of water + X kg of sugar
i.e. 1 litre of this particular solution contains 200 g of sugar per litre of syrup (which seems quite low, actually)
If that logic/math is correct, then (consulting the brix table) my thick-looking syrup is actually a 20% solution. Right?

The syrup is also quite cloudy, so maybe if I heat it a bit the cloudiness will disappear (as one would expect of a good solution) and the syrup will become thinner.

 

[user 6228]

Okay, here's the next conundrum. I have jerry cans with sugar and syrup (some of the sugar didn't dissolve, so it lies packed tightly at the bottom of the jerry can). I carefully pour off the syrup so that the syrup I pour off doesn't contain undissolved granules of sugar. I then weigh/measure the poured-off syrup to determine what percentage the solution is. The syrup is quite thick, so I imagine it will be 3:2 or 2:1 at least.

Now... 2 litres of syrup weighs 2.4 kg.
Then, what is the percentage of sugar in the syrup?

Maths is not my strong point, but my logic says that the water in the syrup weighs 1 kg per litre, so if I can deduct the water weight, I'll be left with the sugar weight.

2 litres of syrup = 2.4 kg
i.e. 1 litre of syrup = 1.2 kg
1 litre of syrup = 1 kg of water + X kg of sugar
i.e. 1 litre of this particular solution contains 200 g of sugar per litre of syrup (which seems quite low, actually)
If that logic/math is correct, then (consulting the brix table) my thick-looking syrup is actually a 20% solution. Right?

The syrup is also quite cloudy, so maybe if I heat it a bit the cloudiness will disappear (as one would expect of a good solution) and the syrup will become thinner.

no ... do it this way

1L =1.2Kg => 1.2 SG l
Then lookup 1.2 SG in the tables we get 44.1 Brix
sugar Kg /L = 0.441*1.2 =0.529 Kg/L

 

[ugcheleuce]

no ... do it this way
1L =1.2Kg => 1.2 SG l
Then lookup 1.2 SG in the tables we get 44.1 Brix
sugar Kg /L = 0.441*1.2 =0.529 Kg/L

Fantastic, you are a great help. This stuff should be on beekeeping sites (or perhaps I'm just the odd one out for doing stuff with syrup that I should not...).

I wonder if you'll be willing to help me even more for the next formula (I'm not lazy, I'm just not good with maths):

It was past midnight and I added too much water to the mixture. In the morning, then the syrup had cooled, I discovered that my syrup is a 44% solution, but... I want to have an 60% solution. This means boiling the syrup (fortunately it's pure sugar cane plus pure water) until enough water evaporates for it to reach 60%.

The SG for 44% brix is 1.2 and the SG for 60% brix is 1.3. By how much should I reduce 1 litre of 44% syrup so that it becomes 60% syrup?

(the same formula could be used in the other direction... if one had 60% syrup, how much water should one add to get 44% syrup)

Thanks in advance
Samuel

 

[alanf]

Both are acceptable.

1 lb sugar + 1 pint water = 44.4% solution
1 lb sugar + 2 pints water = 28.5% solution

In NL the 1:1 solution is a 50% solution (we use kilograms and litres), but spring feeding can be thinner, since the purpose of it isn't to feed sugar but to simulate a nectar flow so that the bees are encouraged to go out -- it can be even thinner, e.g. 1:2 (which in NL would be a 33.3% solution).

Actually, most of us in the UK use kg and litres too. Sugar changed from 2 pound bags to 1 kg bags on the supermarket shelf over 30 years ago. Old books and Americans still use pints and pounds.

Burn the heretic.

 

[user 6228]

Fantastic, you are a great help. This stuff should be on beekeeping sites (or perhaps I'm just the odd one out for doing stuff with syrup that I should not...).

I wonder if you'll be willing to help me even more for the next formula (I'm not lazy, I'm just not good with maths):

It was past midnight and I added too much water to the mixture. In the morning, then the syrup had cooled, I discovered that my syrup is a 44% solution, but... I want to have an 60% solution. This means boiling the syrup (fortunately it's pure sugar cane plus pure water) until enough water evaporates for it to reach 60%.

The SG for 44% brix is 1.2 and the SG for 60% brix is 1.3. By how much should I reduce 1 litre of 44% syrup so that it becomes 60% syrup?

(the same formula could be used in the other direction... if one had 60% syrup, how much water should one add to get 44% syrup)

Thanks in advance
Samuel

volume to unknown volume where amount of sugar is constant and source and destination Brix are known.

volume A @ brix X to volume B @ brix Y

SG(X) = table(brix(X))
weight(A) = vol(A)*SG(X)
sugar(A) = brix(A)*weight(A)

sugar(A) = sugar(B)

weight(B) = sugar(B)/brix(B)
SG(Y) = table(brix(Y))
Vol(B) = weight(B)/SG(Y)



you can use these as steps or substitute to get one equation.

Derek

 

[ugcheleuce]

volume A @ brix X to volume B @ brix Y

SG(X) = table(brix(X))
weight(A) = vol(A)*SG(A)
sugar(A) = brix(A)*weight(A)

sugar(A) = sugar(B)

weight(B) = sugar(B)/brix(B)
SG(Y) = table(brix(Y))
Vol(B) = weight(B)/SG(Y)

Yeah... obvious. Why is the right answer always obvious (but the obvious answer not always the right one)?

(Thanks, by the way.)

 

[alanf]

... This means boiling the syrup (fortunately it's pure sugar cane plus pure water) until enough water evaporates for it to reach 60%....

That would be a very inefficient way of doing it, lots of time and energy. And increases HMF content more than you have to. Just warm it a little and add some more sugar. If you start with 44% by weight, every 100 g has 44 g of sugar and 56 g of water. To make it 60% you need 56 g x 1.5 sugar, so 84 g. Add another 40 g of sugar per 100 g syrup.

 

[ugcheleuce]

That would be a very inefficient way of doing it, lots of time and energy.

It took two hours for 5 litres.

And increases HMF content more than you have to.

Are you sure? I though HMF wouldn't increase if it's pure water and pure cane sugar (sucrose).

Just warm it a little and add some more sugar.

Me don't have more sugar but yes, that would be an easy way to do it.

 

[alanf]

It took two hours for 5 litres...Me don't have more sugar but yes, that would be an easy way to do it.

Turning water to steam takes energy, in an open pot over two hours a couple of kWh per litre I'd guess. It might be cheaper to spend money on sugar rather than energy for a lot of steam and heat you then have to get rid of.

Are you sure? I though HMF wouldn't increase if it's pure water and pure cane sugar (sucrose).

Heat sucrose syrup and it turns into glucose and fructose. Heat fructose and it turns into HMF. It's faster if there's acid present but still happens by just boiling syrup for a couple of hours. Exactly how much depends on such things as local hotspots in the pan because the process accelerates over 100C and how "hard" the water was (dissolved carbonates etc).