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Here are the critical levels for crude oil now

Crude oil's plunge intensified on Tuesday morning, as the commodity broke dramatically below $37 per barrel to hit a seven-year low. And at this point, technically minded traders appear to be eyeing $32 as the next substantial level of support.

"Expect the downward acceleration to continue in oil, after the key $38 level was broken in trading last night," warned Phillip Streible, senior market strategist with RJO Futures. "Margin clerks are probably out sharpening their pencils as forced liquidation could drag that market down to $32 per barrel, causing U.S. producers to feel the pain."

Since futures are traded on margins, declines in price can beget further declines, as those traders who are long can receive margin calls that may force their positions to be liquidated. This has the potential to add unnatural selling pressure to the market.

Rich Ross, head of technical analysis at Evercore ISI, also has $32 as the next line of support.

The $32 level happens to have a bit of history behind it; it is roughly the lowest that oil has traded over the past decade. In January of 2009, crude found a low of $32.70 before turning around.

Read MoreI see oil bottom higher than I did before: Analyst

Others are aiming slightly higher. Piper Jaffray technical analyst Craig Johnson and the commodities brokers at iTrader see support at $33 to $35 and $34 to $35, respectively.

Below the low-$30s levels, it gets a bit hairy. Crude oil hasn't been below $30 since 2003, so finding significant levels of support becomes a bit difficult.

Johnson says only that below $33 to $35, "support is in the $20s."

Todd Gordon of TradingAnalysis.com is a bit more specific, basing his work on potential percentage declines from the highs, rather that levels that are meaningful for historical reasons.

Because oil fell 77 percent during the financial crisis, there is historical precedent for another 77 percent drop, Gordon says. From the $112 peak seen in mid-2013, such a decline would take crude to $26, making that his current target.

Read MoreSaudi Arabia can't afford low oil prices for much longer: SocGen

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